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ELECTRICITY  AND  MAGNETISM 


BY 

FLEEMING  JENKIN,  F.R.SS.  L.  &  E.,  M.I.C.E. 

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PROFESSOR    OF     ENGINEERING 

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D.     APPLETON     AND     CO. 

NEW    YORK. 

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INTRODUCTION. 


WHEN  the  author  was  asked  to  write  the  following 
little  treatise  he  acceded  to  the  request  with  much 
pleasure,  because  he  had  long  known  that  an  ele- 
mentary treatise  on  Electricity  and  Magnetism  of  a 
somewhat  novel  character  was  much  needed.  In 
England  at  the  present  time  it  may  almost  be  said 
that  there  are  two  sciences  of  Electricity — one  that 
is  taught  in  ordinary  text-books,  and  the  other  a 
sort  of  floating  science  known  more  or  less  perfectly 
to  practical  electricians,  and  expressed  in  a  fragmentary 
manner  in  papers  by  Faraday,  Thomson,  Maxwell, 
Joule,  Siemens,  Matthiessen,  Clark,  Varley,  Culley, 
and  others.  The  science  of  the  schools  is  so  dis- 
similar from  that  of  the  practical  electrician  that  it 
has  been  quite  impossible  to  give  students  any 
sufficient,  or  even  approximately  sufficient,  text-book. 
It  has  been  necessary  to  refer  them  to  disjointed 
treatises  in  the  Reports  of  the  British  Association,  in  the 
'  Cambridge  Mathematical  Journal/  the  '  Phil.  Trans.' 
and  the  'Phil.  Magazine.'  A  student  might  have 
mastered  Delarive's  large  and  valuable  treatise  and 

869471 


vi  Introduction. 

yet  feel  as  if  in  an  unknown  country  and  listening  to 
an  unknown  tongue  in  the  company  of  practical  men. 
It  is  also  not  a  little  curious  that  the  science  known 
to  the  practical  men  was,  so  to  speak,  far  more  scientific 
than  the  science  of  the  text-books.  These  latter 
contain  an  apparently  incoherent  series  of  facts,  and 
it  is  only  by  some  considerable  mental  labour  that, 
after  reading  the  long  roll  of  disjointed  experiments, 
the  student  can  even  approximately  understand  any 
one  experiment  in  its  entirety ;  the  explanation  of 
part  of  the  very  first  phenomenon  described  cannot 
be  given  until  one  of  the  very  last  experiments  has 
been  mastered. 

The  author  has  found  it  quite  impossible,  for  this 
very  reason,  to  write  his  treatise  on  the  ordinary  plan 
of  beginning  with  simple  experiments  and  gradually 
building  up  a  science  by  the  description  of  a  series  of 
more  and  more  complex  phenomena.  Not  a  single 
electrical  fact  can  be  correctly  understood  or  even 
explained  until  a  general  view  of  the  science  has 
been  taken  and  the  terms  employed  defined.  The 
terms  which  are  employed  imply  no  hypothesis,  and 
yet  the  very  explanation  of  them  builds  up  what  may 
be  called  a  theory.  The  terms  cannot  be  explained 
by  mere  definitions,  because  they  refer  to  phenomena 
with  which  the  reader  is  unacquainted.  The  mere 
explanation  of  the  terms,  therefore,  requires  some 
rapid  description  of  facts,  the  truth  of  which  the 
reader  must  at  first  take  for  granted.  Many  of  the 


Introduction.  vii 

assertions  cannot  be  proved  to  be  true  except  by 
complex  apparatus,  and  the  action  of  this  complex 
apparatus  cannot  be  explained  until  the  general 
theory  has  been  mastered. 

The  plan  followed  in  the  book  is  therefore  as 
follows : — First,  a  general  synthetical  view  of  the 
science  has  been  given,  in  which  the  main  phenomena 
are  described  and  the  terms  employed  explained.  This 
general  view  of  the  science  cannot  be  made  very  easy 
reading,  although  it  will  probably  be  found  easier  by 
those  who  have  no  preconceived  notions  about  tension, 
intensity,  and  so  forth,  than  by  students  of  old  text- 
books. If  this  portion  of  the  work  can  be  mastered, 
the  student  will  then  be  readily  able  to  understand 
what  follows,  viz.,  the  description  of  the  apparatus 
used  to  measure  electrical  magnitudes  and  to  produce 
electricity  under  various  conditions.  The  difference 
between  the  Electricity  of  schools  and  of  the  testing 
office  has  been  mainly  brought  about  by  the  absolute 
necessity  in  practice  for  definite  measurement.  The 
lecturer  is  content  to  say,  under  such  and  such  cir- 
cumstances, a  current  flows  or  a  resistance  is  increased. 
The  practical  electrician  must  know  how  much  current 
and  how  much  resistance,  or  he  knows  nothing ;  the 
difference  is  analogous  to  that  between  quantitative 
and  qualitative  analysis.  This  measurement  of  elec- 
trical magnitudes  absolutely  requires  the  use  of  the 
word  and  idea  potential,  and  of  various  units  each 
with  an  appropriate  name,  in  terms  of  which  each 


viii  Introduction. 

electrical  magnitude  can  be  expressed.  On  a  proper 
choice  of  units  depends  the  simplicity  of  the  ex- 
pression for  the  laws  which  connect  electrical  phe- 
nomena. After  describing  these  laws  and  measure- 
ments, the  author  has  given  their  chief  practical 
application  to  telegraphy  and  a  few  examples  of  the 
construction  of  telegraphic  apparatus.  These  fluctuate 
in  form  from  year  to  year,  and  the  special  forms  now 
in  use  will  soon  become  antiquated ;  but  the  general 
theory  of  Electricity  on  which  the  construction  and 
use  of  these  depends  is  permanent,  depending  on  no 
hypothesis,  and  it  has  been  the  author's  aim  to  state 
this  general  theory  in  a  connected  manner  and  in 
such  a  simple  form  that  it  might  be  readily  under- 
stood by  practical  men. 


The  above  introduction  is  allowed  to  stand  un- 
altered because  it  correctly  describes  what  the  author 
aimed  at.  He  feels  that  the  actual  book  falls  very 
far  short  of  the  ideal  he  had  conceived  ;  he  perceives 
only  too  well  that  the  arrangement  might  be  very 
greatly  improved,  and  the  statements  made  in  much 
clearer  language.  The  book  has  been  unfortunately 
written  in  intervals  snatched  from  professional  en- 
gagements at  irregular  periods,  but  the  author  would 
rather  claim  indulgence  on  the  score  that  the  effort 
made  has  at  least  been  in  the  right  direction,  although 
far  from  fully  successful. 


Introduction.  ix 

He  has  to  acknowledge  having  received  very  kind 
assistance  from  his  friends  Sir  W.  Thomson,  Professor 
J.  C.  Maxwell,  Mr.  Culley,  and  Mr.  C.  F.  Varley ;  as 
well  as  from  three  of  his  assistants,  Mr.  W.  Bottomley, 
Mr.  W.  E.  Ayrton,  and  Mr.  W.  F.  King,  who  kindly 
examined  the  proofs. 

Mr.  Latimer  Clark  and  Mr.  Culley  have  allowed 
free  use  to  be  made  of  extracts  from  their  valuable 
handbooks. 


CONTENTS. 


CHAPTER  I. 
ELECTRIC    QUANTITY. 

PAGE 

I.  Definition  of  Electricity,  and  how  it  is  produced  by  Friction  ;  I 
Conductors,  Insulators.  §  2.  Resinous  and  Vitreous  Electricity  ; 
Attractions  and  Repulsions  ;  meaning  of  a  Charge.  §  3. 
Quantity  of  Electricity  ;  depends  on  the  measurement  of  Force. 
§  4.  Experiments  illustrating  the  foregoing  ;  Electroscope.  §  5. 
Electricity  at  rest  resides  on  the  Surface  of  Conductors.  §  6. 
Justification  of  the  names  positive  and  negative  Electricity. 
§  7.  Attraction  and  Repulsion  between  Bodies  positively  and 
negatively  electrified.  §  8.  When  Electricity  is  produced,  equal 
quantities  of  positive  and  negative  Electricity  are  produced.  §  9. 
Electric  Series  or  List  determining  the  sign  of  the  Electricity  pro- 
duced by  Friction.  §  10.  Preliminary  Explanation  of  the  word 
Potential.  §  n.  Statical  Induction.  §  12.  The  existence  of 
any  Charge  implies  an  equal  and  opposite  induced  Charge. 
§  13.  Induction  implies  two  Conductors  at  different  Potentials 
separated  by  Insulators.  §  14.  Attractions  and  Repulsions  con- 
sidered as  due  to  Induction.  §  15.  Distribution  of  Electricity 
examined  by  Proof  plane.  §  16.  Electrification  does  not  imply 
Charge  at  all  points  of  Surface  ;  Leyden  Jar  or  Condenser. 
§  17.  Meaning  of  the  measurement  of  a  quantity  of  Electricity. 
§  1 8.  Absolute  Electrometer  measures  Quantity.  §  19.  Pro- 
duction of  Electricity  by  other  means  than  Friction ;  galvanic 
Cell.  §  20.  Identity  of  Electricity,  however  produced.  §  21. 
Electricity  produced  by  contact  of  Insulators.  §  22.  Electricity 
produced  by  unequal  distribution  of  Heat.  §  23.  Effect  of  a 
Metal  Screen  between  two  electrified  Bodies  .  .  .  .26 


xii  Contents. 

CHAPTER   II. 
POTENTIAL. 

PAGE 

§  I.  Definition  of  Difference  of  Potentials.  §  2.  Work  done  in  26 
moving  Electricity  from  one  Point  to  another  is  not  affected  by 
Path  followed.  §  3.  Constant  Potential.  §  4.  The  Potential 
of  a  Body  is  the  difference  of  its  Potential  from  that  of  the 
Earth.  §  5.  On  what  electric  Potential  depends.  §  6.  Mean- 
ing of  higher  and  .lower  Potential.  §  7.  Illustration  of 
foregoing ;  Surface  and  Interior  of  electrified  Conductor.  §  8. 
Space  round  charged  Conductor.  §  9.  Illustration  by  Leyden 
Jar.  §  10.  More  complex  Illustration.  §  n.  Effect  of  Changes 
of  electrification  of  Leyden  Jar  on  Potentials  of  the  several  parts. 
Effect  of  connecting  two  Jars.  §  13.  Relation  between  Charge 
and  Potential.  §  14.  Immaterial  which  coating  of  Leyden  Jar 
is  to  Earth.  §  15.  Theory  of  Electroscopes.  §  16.  Flow  of 
Electricity  determined  by  difference  of  Potential.  §17.  Effect 
of  joining  a  Conductor  by  a  Wire  with  a  Point  of  no  Capacity 
but  of  different  Potential.  §  18.  Electricity  in  motion  always 
does  work.  §  19.  Difference  of  Potential  produced  by  Induction. 
§  20.  Difference  of  Potential  produced  by  Friction.  §  21.  Dif- 
ference of  Potential  produced  by  Contact ;  Electric-contact  Series 
or  List  of  Conductors.  §  22.  Analogies  and  differences  in  the  re- 
sult of  contact  in  the  cases  of  Solids  and  Liquids  ;  Galvanic-cell ; 
.Electrolytes;  Electrolysis.  §  23.  Electromotive  Force,  E.  M.  F. 
§  24.  It  is  affected  by  Temperature.  §  25.  Currents  of  Elec- 
tricity and  Magnetism  can  produce  E.  M.  F.  §  26.  Unit  of 
E.  M.  F.  or  difference  of  Potential 52 

CHAPTER   III. 

CURRENT. 

§  I  Definition  of  voltaic  or  galvanic  Current.  §  2.  Transient  and  52 
permanent  Currents.  §  3.  Currents  involve  the  performance  of 
work.  §  4.  Is  the  Current  due  to  contact  or  chemical  action  ? 
§  5.  Why  no  arrangement  of  Metals  without  Electrolytes  can 
give  a  Current.  §  6.  Attractions  and  Repulsions  between  Cur- 
rents. §  7.  Verification  of  Statements  by  Experiments  ;  rectangle 
and  straight  Wire.  §  8.  One  Rectangle  inside  another.  §  9. 


Contents.  xiii 


PAGE 


Multiplication  of  effect  by  multiplying  the  number  of  turns  made 
by  the  Wires  ;  Electro-dynamometer.  §  10.  Solenoids  and  fla 
Coils.  §  1 1.  Analogy  between  Magnets  and  Solenoids  ;  Galvano- 
meters and  Galvanoscopes.  §12.  Simplest  form  of  Mirror  Gal- 
.vanometer.  §  13.  Magnetization  of  Iron  by  Currents.  §  14.  A 
Current  heats  the  conducting  Wire;  amount  of  Heat.  §  15. 
Electrolysis  described  ;  Ions,  Anode  Kathode  ;  electrolysis  of 
Water.  §  16.  Effect  produced  by  Currents  traversing  bad  Con- 
ductors. §  1 7.  Analogy  between  effect  of  Current  on  Magnet 
and  effect  of  Current  of  Water  in  Pipe  on  a  Piston.  §  18.  One 
Current  can  induce  another;  this  is  explained  by  the  above  analogy. 
§  19.  Direction  of  the  induced  Current  under  various  Circum- 
stances ;  distinction  between  electromagnetic  and  electrostatic 
Induction,  §  20.  Induction  due  to  the  increase  or  decrease  of 
a  Current.  §21.  Reaction  of  the  induced  on  the  inducing  Cur- 
rent. §  22.  Induction  in  a  Circuit  which  is  not  closed.  §  23. 
Case  where  the  closed  Circuit  is  long  and  of  sensible  Capacity. 
§  24.  Strength  of  constant  Current  equal  in  all  parts  of  Circuit. 
§  25.  Currents  are  not  constant  in  all  parts  of  Circuit  when  they 
start  and  cease.  §  26.  Thermo-electric  Currents.  §  27.  Resume 
of  the  several  Causes  which  produce  Currents  .  .  .  .  80 


CHAPTER   IV. 

RESISTANCE. 

I.  Meaning  of  Resistance.  §  2.  Definition  of  Resistance  ;  8 1 
Ohm's  Law.  §  3.  Relations  between  Resistance  and  Dimen- 
sions of  Conductor  ;  comparison  of  Resistance  by  differential 
Galvanometer.  §  4.  Relation  between  Resistance  and  Weight 
per  Unit  of  length  of  Conductor.  §  5.  Effect  of  Temperature 
on  Resistance.  §  6.  Object  of  determining  Resistance.  §  7- 
Effect  of  Changing  Resistance  of  Parts  of  a  Voltaic  Circuit ; 
Cells  joined  in  Series  and  Multiple  Arc.  §  8.  Effect  of  Resist- 
ance of  Galvanometer.  §  9.  Apparent  Resistances  which  are 
not  really  Resistances.  §  10.  Polarisation  of  Insulators.  §  II. 
Resistance  of  Air  to  Sparks  or  Brushes  not  subject  to  Ohm's 
Law.  §  12.  Resistance  of  Rarefied  Gases  .  .  .  -93 


xiv  Contents. 

CHAPTER   V. 

ELECTRO-STATIC   MEASUREMENT. 

PAGE 

§  I.  Fundamental  Units.  §  2.  Definition  of  Unit  Quantity,  Unit  94 
Difference  of  Potentials  and  Unit  Resistance.  §  3.  Relation 
between  Force  of  Attraction  or  Repulsion  and  Quantity  of 
Electricity.  §  4.  Definition  of  Capacity  ;  Expression  for  Capa- 
city of  simple  geometrical  Forms.  §  5.  Capacity  of  Conduc- 
tors ;  specific  inductive  Capacity  of  Materials  ;  Table.  §  6. 
Effect  of  polarisation  or  absorption  on  Capacity  of  Condensers. 
§  7.  Experimental  Measurement  of  Difference  of  Potential  be- 
tween two  opposed  Plane  Surfaces  by  Thomson's  guard  ring 
Electrometer.  §  8.  Electromotive  Force  of  Daniell's  Voltaic 
Cell.  §  9.  Capacity  of  long  cylindrical  Conductor  ;  Subma- 
rine Cable.  §  10.  Electric  Density;  electrostatic  Force.  §  II, 
Diminution  of  air  pressure  in  consequence  of  Electricity  on 
Surface  of  Conductor  ;  Table  giving  Relation  between  Electro- 
static Force  and  Sparks  from  convex  Plates.  §  12.  Effects  of 
silent  Discharge  or  Brush  and  Sparks  from  Points.  §  13. 
General  Ideas  on  distribution  of  Electricity.  §  14.  Material 
representation  of  electrostatic  Units.  §  15.  Equations  ex- 
pressing Relations  between  electrostatic  Units.  Unit  of  Cur- 
rent in  electrostatic  Measure 109 


CHAPTER   VI. 
MAGNETISM. 

I.  Description  of  a  Magnet.  §  2.  Definition  of  north  and  109 
south  Poles  ;  the  Earth  a  Magnet.  §  3.  Definition  of  the 
strength  of  a  Pole  and  of  Unit  Pole.  §  4.  Magnetic  Field ; 
intensity  of  Field ;  lines  of  Force.  §  5.  Lines  of  Force  from 
Single  Pole  and  in  uniform  Field.  §  6.  Couple  acting  on 
Magnet  in  uniform  Field ;  Magnetic  Moment ;  Intensity  of 
Magnetisation.  §  7.  Magnetism  produced  by  magnetic  In- 
duction ;  paramagnetic  and  diamagnetic  Bodies.  §  8.  Effect 
of  laying  bar  Magnets  side  by  side.  §  9.  Residual  Magnetism 
and  coercive  Force.  §  10.  Magnetic  Potential ;  equipotential 
Surfaces.  §  II.  Faraday's  Lines  of  Force  completely  map  out 


Contents.  xv 


magnetic  Field.  §  12.  Magnetic  Fields  due  to  single  Pole 
and  to  single  long  straight  Current.  §  13.  Importance  of  a 
Knowledge  of  magnetic  Fields  in  practical  Telegraphy.  §  14. 
Position  of  Poles  in  bar  Magnets  ;  the  fragments  of  a  Magnet 
are  Magnets  ;  a  Magnet  induces  Poles  in  all  Bodies  which  it 
attracts.  §  15.  How  Magnets  are  made.  §  16.  Electro-mag- 
nets ;  ring  Magnets  produce  no  magnetic  Field.  §  17.  Mag- 
netic Moment  of  a  long  thin  Bar  and  of  a  Sphere  in  Terms  of 
Intensity  of  magnetic  Field.  §  18.  Coefficient  of  magnetic  In- 
duction for  Iron.  §  19.  Coefficient  of  magnetic  Induction  for 
other  Materials.  §  20.  Coefficient  of  Magnetic  Induction  for 
paramagnetic  Bodies.  §  21.  Attraction  between  a  Magnet  and 
Armature  ..........  125 


CHAPTER   VII. 
MAGNETIC   MEASUREMENTS. 

I.  Introduction  to  Measurement  of  magnetic  Phenomena  in  ab-  126 
solute  Measure.  §  2.  Magnetic  Meridian  ;  magnetic  Declina- 
tion ;  magnetic  Inclination ;  Dip.  §  3.  Periodic  Changes  in 
Earth's  Magnetism  ;  isoclinic  Lines.  §  4.  Horizontal  Compo- 
nent of  Earth's  Magnetism.  §  5.  Determination  of  magnetic 
Moment  of  a  Magnet  and  of  horizontal  Component  H  of  Earth's 
Magnetism.  §  6.  Single  Experiment  will  determine  mag- 
netic Moment  of  Bar  in  terms  of  H.  §  7.  Units  to  be  employed 
in  above  Measurements.  §  8.  How  to  find  Moment  of  Inertia 
of  a  given  Weight  ;  Comparison  of  magnetic  Moments.  §  9. 
Difference  between  real  Magnet  and  hypothetical  Magnet  .  133 


CHAPTER   VIII. 
ELECTRO-MAGNETIC    MEASUREMENT. 

§  I.  Electro-magnetic  System  of  Units  based  on  action  of  Currents  133 
on  Magnets  ;  Definition  of  unit  Current.  §  2.  Ratio  between 
electrostatic  and  electro -magnetic  Series.  §  3.  Tangent  Galva- 
nometer used  to  measure  Current  in  electro-magnetic  Measure. 
§  4.  Ampere's  Theory  of  the  action  of  Currents  on  Currents. 
§  5.  Weber's  Electrodynamometer.  §  6.  Kohlrausch's  Method 


xvi  Contents. 


PAGE 


of  measuring  Current.  §  7.  Action  between  Rings  conveying 
Currents  in  parallel  Planes.  §  8.  Magnetic  Field  produced  by 
Current  in  a  long  Helix.  §  9.  Theory  of  the  Solenoid.  §  10. 
Sucking  action  of  Solenoid  on  Bar  of  Iron  partially  covered  by 
it.  §  II.  Difference  between  hollow  Magnet  and  Solenoid. 
§  12.  Effect  of  introducing  soft  iron  Wire  into  a  Solenoid  .  146 


CHAPTER   IX. 
MEASUREMENT  OF   ELECTRO-MAGNETIC   INDUCTION. 

I.  Electro-magnetic  Force  experienced  by  a  Wire  moving  in  a  147 
magnetic  Field.  §  2.  Electromotive  Force  produced  in  a  Wire 
so  moving.  §  3.  Illustration  of  the  foregoing.  §  4.  Rotation 
of  a  Coil  in  a  magnetic  Field.  §  5.  Determination  of  the  Re- 
sistance of  a  Conductor  in  electro-magnetic  Measure  by  the  ro- 
tation of  a  Coil  in  a  magnetic  Field.  §  6.  Second  Method 
adopted  by  electrical  Standards  Committee  of  British  Associ- 
ation for  Advancement  of  Science.  §  7.  Electromotive  Force 
produced  in  a  Wire  by  the  increase  or  decrease  of  Current  in  a 
neighbouring  Wire.  §  8.  Mathematical  Expression  for  this 
E.  M.  F.  §  9.  Measurement  of  electric  Quantity  in  electro- 
magnetic Measure.  §  10.  General  Deductions  applicable  to 
Practice 157 


CHAPTER  X. 

UNITS   ADOPTED    IN   PRACTICE. 

I.  British  Association  Standard  of  Resistance.  §  2.  Practical  158 
Units  of  electromotive  force  and  Capacity.  §  3.  Practical  Units 
are  all  intended  to  be  Multiples  of  absolute  electro-magnetic 
Units.  §  4.  Units  of  Current  and  Quantity  ;  Ohm,  Volt, 
and  Farad ;  Farad  per  Second.  §  5.  Multiples  and  Sub- 
multiples;  Dimensions  of  Units;  Table  of  Units  compared 
with  absolute  Measure  ;  Table  of  Dimensions  of  Units  ;  useful 
Constants  for  the  conveision  of  Measurements  expressed  in 
Terms  of  one  Series  of  fundamental  Units  into  Measurements 
based  on  another  fundamental  Series  .  .  .  .  .165 


Contents.  xvii 

CHAPTER   XI. 
CHEMICAL   THEORY   OF    ELECTROMOTIVE    FORCE. 

PAGK 

I.  Electrolysis.  §  2.  Electro-positive  and  electro-negative  Ions.  166 
§  3.  Electrolysis  of  Salts.  §  4.  Electro-chemical  Series ; 
Table.  §  5.  Electro-chemical  Equivalents  ;  Table.  §  6. 
Relation  between  Work  done  by  the  Current  and  Electro- 
lysis. §  7.  Measurement  of  chemical  Affinity  by  electro- 
motive Force  required  for  Electrolysis.  §  8.  Calculation  of 
electromotive  Force  produced  by  a  Combination,  in  Terms  of 
the  heat  of  Combination.  §  9.  Electromotive  Force  of  Daniell's 
Cell  calculated  from  chemical  Action.  §  10.  Practical  Appli- 
cations of  Electrolysis.  §  1 1.  Mode  of  Transfer  of  Ions  through 
the  Electrolyte  .  .  .  . 174 

CHAPTER   XII. 
THERMO-ELECTRICITY. 

i.  Definition  of  Thermo-electric  Power  of  a  Circuit  of  two  174 
Metals.  §  2.  Thermo-electric  Series  ;  Table.  §  3.  Electromo- 
tive Force  of  a  thermo-electric  Pair  producing  a  Current  in  a 
complex  Circuit.  §  4.  Variations  in  thermo-electric  Series  due 
to  change  of  Temperature ;  Diagram.  §  5.  Calculation  of 
E.M.F.  of  a  thermo-electric  Pair  from  their  thermo-electric 
Powers  at  different  Temperatures.  §  6.  Neutral  Points.  §  7., 
Professor  Tait's  Law  ;  Calculation  of  E.  M.  F.  of  a  thermo-electric 
Pair  from  Diagram  and  from  Table.  §  8.  Addition  of  Electro- 
motive Forces  of  Pairs  arranged  in  Series.  §  9.  Thermo  electric 
Action  of  non-metallic  Substances.  §  10.  Measurement  of 
Temperature  by  Thermo-electric  Batteries.  §  u.  Peltier's  Law 
of  absorption  and  evolution  of  Heat  at  the  Junctions.  §  12. 
Sir  William  Thomson's  Law;  absorption  and  evolution  of  Heat 
at  other  parts  of  the  Circuit 187 

CHAPTER   XIII. 
GALVANOMETERS. 

I.  General  Description  and  Classification.      §  2.  Galvanoscopes  187 
with  vertical  weighted  Needles.       §    3.   Relation   between  the 
Circuit  and  Class  of  Galvanometer  to  be  employed  ;  long  Coils 
a 


Contents. 


PACK 

and  short  Coils  ;  Intensity  and  Quantity.  §  4.  Equal  Deflec- 
tions on  any  constant  Galvanometer  indicate  equal  Currents. 
§  5.  How  to  measure  and  regulate  the  sensibility  of  Galvano- 
meters. §  6.  Astatic  Galvanometers.  §  7.  Tangent  Galvano- 
meters. §  3.  Sine  Galvanometers.  §  9.  Best  form  of  Coil  for 
mirror  Galvanometers.  §  10.  Graded  Galvanometers.  §  u. 
Dead  beat  Galvanometers.  §  12.  Marine  Galvanometers.  §13. 
Differential  Galvanometers.  §  14.  Shunts  used  to  vary  Sensi- 
bility. §  !$•  General  Remarks  on  constructive  Details  .  .  203 


CHAPTER   XIV. 
ELECTROMETERS. 

I.  General  Description  ;  Canton's,  Bennet's,  Peltier's,  Bohnen-  203 
berger's,      heterostatic     Electrometers.       §    2.     Sir     William 
Thomson's  quadrant   Electrometer.      §  3.    Sir  W.  Thomson's 
portable  Electrometer.     §4.  Absolute  Electrometers         .         .211 

CHAPTER  XV. 
GALVANIC    BATTERIES. 

I.  Single  fluid  Cell;  common  zinc  and  copper  Cell;  sand  211 
Battery ;  Smee's  and  Walker's.  §  2.  Points  of  Merit  in  a  gal- 
vanic Cell.  §  3.  Polarisation  by  deposition  of  Gas  on  Plates 
of  Cells.  §  7.  Local  action  causing  waste  of  Zinc  ;  amalga- 
mation of  Zinc.  §  8.  Inconstancy  of  Solution  in  single  fluid 
Cell.  §  9.  Daniell's  Cell ;  Double  Fluid.  §  10.  Theory  of 
Daniell's  Cell.  §  u.  Practical  management  of  Daniell's  Cell. 
§  12.  Large  Forms  of  Daniell's  Cell ;  sawdust  Cells.  §  13. 
Sir  William  Thomson's  or  Menotti's  sawdust  Cell ;  gravitation 
Cell.  §  14.  Marie  Davy's,  Grove's,  Bunsen's,  Faure's  Cells ; 
Chromate  of  Potassium  Element ;  Leclanche's  Cell ;  L.  Clark's 
Cell.  §15.  Practical  Management  of  a  galvanic  Battery  .  .  228 

CHAPTER   XVI. 
MEASUREMENT   OF   RESISTANCE. 

J.  Arrangement  and  construction  of  Boxes  of  resistance  Coils.   229 
§  2.  Alternative  Arrangements  and  practical  Details.     §  3.    Use 
of  Shunts.     §  4.  Definition  of  Conductivity  ;  addition  of  Con- 


Contents.  xix 

PACK 

ductivities.  §  5.  Comparison  of  Resistances  by  Comparison  of 
Deflections  on  Galvanometers.  §  6.  Extension  of  this  Method 
by  the  use  of  Shunts  ;  Tests  of  Insulation  of  Core  of  Submarine 
Cables.  §  7.  Four  Methods  of  determining  the  Resistance  of 
a  Battery.  §  8.  Comparison  of  Resistances  by  shunted  diffe- 
rential Galvanometer.  §  9.  Potential  at  different  Points  of  a 
Conductor  through  which  a  permanent  Current  is  flowing. 
§  10.  No  Current  flows  through  a  Wire  conecting  two  Points 
of  two  Circuits  if  these  Points  are  at  one  Potential ;  this 
Law  allows  us  to  divide  two  Conductors  of  different  resist- 
ances in  one  and  the  same  ratio.  §  n.  Measurement  of 
Resistance  by  Wheatstone's  Balance  or  Bridge.  §  12.  Kirch- 
hoff's  Laws.  §  13.  Theory  of  Bridge  deduced  from  Kirch- 
hoff 's  Laws.  §  14.  Specific  resistance  of  Materials  ;  Defini- 
tion ;  Table  for  Metals.  §  15.  Specific  Conductivity.  §  16. 
Effect  of  Temperature  on  specific  resistance  of  Metals.  §  17. 
Specific  resistance  of  Insulators,  Gutta-percha,  India-rubber ; 
Electrification.  §  18.  Measurement  of  resistance  of  Insulators 
by  loss  of  Charge.  §  19.  Effect  of  Temperature  on  specific 
resistance  of  Insulators.  §  20.  Specific  resistance  of  Miscel- 
laneous Insulators.  §  21.  Graphite,  gas  Coke,  Tellurium  Phos- 
phorus. §  22.  Specific  resistance  of  liquid  Electrolytes..  §  23. 
Precautions  to  be  observed  when  measuring  high  Resistances  .  2§i 

CHAPTER   XVII. 
COMPARISON  OF    CAPACITIES,    POTENTIALS,  AND   QUANTITIES. 

§  I.  Comparison  of  Capacities  by  relative  Throws  of  Galvano-  261 
meter  ;  ballistic  pendulum  Formula.  §  2.  Effect  of  shunting 
Galvanometer.  §  3.  Differential  Methods  with  Galvanometer 
and  resistance  Slides.  §  4.  Comparison  by  Platymeter.  §  5. 
Absolute  Capacity  from  ballistic  Formula.  §  6.  Comparison 
of  Potentials.  §  7.  Comparison  of  Quantities  ....  268 

CHAPTER   XVIII. 
FRICTIONAL    ELECTRICAL   MACHINES. 

§  2.  Electrophorus.    §  2.   Common  frictional  Machine.    §  3.   Con-  268 
ductors  or  Condensers  used  with  frictional  Machines.     §  4.   Sir 
William  Armstrong's  Machine  producing  Electricity  by  Steam 
issuing  in  $.  Jet        .........  273 


xx  Contents. 

CHAPTER  XIX. 
ELECTRO-STATIC    INDUCTIVE   MACHINES. 

§  I.  C.  F.  Varley's  Arrangement ;  Sir  William  Thomson's  repleiv   273 
isher  and  Mouse  Mill.     §  2.   Holtz  electrical  Machine       .         .  279 

CHAPTER  XX. 
MAGNETO-ELECTRICAL   APPARATUS. 

§  I.  Definitions.  §  2.  Pixii  or  Clarke's  Apparatus.  §  3.  Rise  279 
and  Fall  of  induced  Current.  §  4.  Mr.  T.  Holmes'  Apparatus. 
§  5.  Limit  of  Current.  §  6.  Mr.  Wild's  and  Mr.  Judd's 
Apparatus.  §  7.  Siemens'  Arrangement.  §  8.  Magneto  signal- 
ling Keys.  §  9.  Inductorium,  or  Ruhmkorffs  Coil.  §  10.  Siemens' 
large  Inductorium  ;  Discharges  through  Geissler  Tubes  .  .291 

CHAPTER   XXI. 
ELECTRO-MAGNETIC   ENGINES. 

§  I.   Elementary  Combinations  in  which  action  between  Currents  291 
produces  Rotation.     §  2.   Rotation  of  Magnet  caused  by  action 
of  Current.      §  3.    -Electromotors  ;    Froment's    Engine  ;  beam 
Engine.     §  4.   Relative  Economy  of  heat  Engines  and  Electro- 
motors  . 296 

CHAPTER  XXIL 
TELEGRAPHIC   APPARATUS. 

§.  r.  Classification  of  Instruments,  Class  I.  and  Class  II.  §  2.  De-  296 
scription  of  telegraphic  Circuit.  §  3.  Elements  of  which  tele- 
graphic Alphabets  are  compounded ;  Class  I.  §  4.  Morse 
Alphabet.  §  5.  Morse  Apparatus  ;  Ink-writer  ;  Bain's  System, 
or  electro-chemical  Morse.  §  6.  Single  Needle ;  Bell.  §  7. 
Relays.  §  8.  Double-current  System.  §  9.  Return  Currents ; 
Discharging  Keys.  §  10.  General  Remarks  on  Design  of 
Telegraphic  Apparatus.  §  II.  Magneto  Senders.  §  12.  Rate 


Contents.  xxi 

PAGE 

of  working ;  Wheatstone's  automatic  Transmitter.  §  13. 
Class  II. ;  Step  by  step  dial  Instruments ;  Siemens'  and 
Wheatstone's.  §  14.  Step  by  step  Printers.  §  15.  Hughes' 
printing  Instrument.  §  16.  Bakewell's  and  Caselli's.  §  17. 
Duplex  System ;  Steam's,  Siemens',  Frischen's.  §  18.  Bells  .  327 


CHAPTER  XXIII. 
SPEED    OF   SIGNALLING. 

§  I.  Velocity  of  Electricity  ;  Retardation  ;  Law  of  Variation  in  327 
the  incipient  Current ;  arrival  Curve  ;  Result  of  successive 
Signals.  §  2.  Effect  of  rapidly  alternating  Currents.  §  3. 
Retardation  on  land  Lines.  §  4.  Retardation  on  Sub-maiine 
Cables  ;  use  of  mirror  Galvanometer  as  receiving  Instrument. 
§  5.  Sir  William  Thomson's  siphon  Recorder.  §  6.  Valley's 
System  of  signalling  by  Condensers  ;  recorder  Alphabet.  §  7. 
Speed  of  working  with  various  Instruments  and  Lines  .  .  338 

CHAPTER   XXIV. 
TELEGRAPHIC   LINES." 

§  i .  General  Description.  §  2.  Sizes  of  iron  Wire  used  for  land  338 
Lines  ;  Poles.  §  5.  Insulation  of  land  Lines  ;  Designs  for 
Insulators  ;  Objects  aimed  at  in  Design.  §  4.  Danger  of  Con- 
tact between  adjacent  Wires.  §  5.  Effect  of  uniform  Leakage 
on  received  Current ;  allowable  Leakage.  §  6.  Description  of 
submarine  insulated  Conductor  ;  Resistance  per  Knot  of  Con- 
ductor ;  Insulation  Resistance  of  insulating  Sheath  ;  Constants 
for  Gutta-percha  and  Hooper's  Material.  §  7.  Capacity  per 
Knot  of  submarine  Cables.  §  8.  Anglo-American  Type  of 
Cable  ;  other  Types  of  Cable 349 

CHAPTER   XXV. 
FAULTS    IN   TELEGRAPHIC    LINES. 

§  i.   Classification  of  Faults.    §  2.  -How  to  find  Position  of  a  Fault  349 
causing  a  Leak  to  Earth.     §  3.   Second  Method.     §  4.  Third 
Method  by  Wheatstone  Bridge  when  there  is  a  return  Wire. 

b 


xxii  Contents. 

PAGF 

§  5.  Determination  of  Position  of  a  small  Fault  by  simultaneous 
Tests  at  both  Ends  of  Line.  §  6.  Effect  of  Faults.  §  7.  Fault 
involving  loss  of  Continuity.  §  8.  Fault  produced  by  Contact 
between  adjacent  Conductors  ......  356 


CHAPTER  XXVI. 

USEFUL   APPLICATIONS    OF    ELECTRICITY   OTHER   THAN 
TELEGRAPHIC. 

i.     Classification.     §   2.    Electro-metallurgy  ;    Electro-plating.   357 
§  3.   Reproduction  of  Objects.       §  4.   Reduction  of  Minerals ; 
Electrolysis.      §  5.   Electric  Light ;  Holmes'  Lamp  ;  Waring's 
Light.     §  6.  Firing  of  Mines  ;  Fuses.     §  7.  Medical  Applica- 
tions.    §  8.   Clocks,  Governors,  and  Chronoscopes  .          .         .   364 


CHAPTER  XXVII. 
ATMOSPHERIC   AND    TERRESTRIAL    ELECTRICITY. 

I.   Distribution  of  Electricity  on  Surface  of  Earth.     §  2.  Earth  365 
Currents.     §  3.   Examination  of  Potential  of  the  Atmosphere  by 
Flame-bearing  or  Water-dropping  Apparatus.     §  4.   Connexion 
between  earth  Currents  and  Magnetism.  ....   367 

CHAPTER  XXVIII. 


I.   General  Description.     §  2.  Deviation  from  Magnetic  Meri-  367 
dian  ;  Methods  of  Correction 368 


APPENDIX  ON  THE  TELEPHONE  AND  MICROPHONE  371 


LIST     OF     TABLES. 


PAGH 

Insulators  relatively  electro-positive  and  electro-negative        .         .       9 
Metals,  potential  or  contact  series        ......     43 

Specific  inductive  capacity  of  insulators         .         .         .         .         .     97 

Sparks,  length  of,  with  given  electro-motive  force         .         .         .    104 
Magnetic  induction,  coefficient  of,  in  various  solids       .         .         .124 
Magnetic  induction,  coefficient  of,  in  various  liquids      .         .         .124 
Force  attracting  magnet  introduced  into  coil  conveying  current      .    145 
Units,  relative  values  of  .         .         .         .         .         .         .162 

Dimensions  of  units    .         .         .         .'         .  .         .         .163 

British  into  metrical  units,  table  for  conversion  of         .         .         .164 
Metrical  into  British  units,  table  for  conversion  of         .         .         .164 
Electro-chemical  series  (ions)       .         .         .         .         .         .         .168 

Electro-chemical  equivalents        .......    169 

Thermo-electric  series .   1 76 

Thermo-electric  table  giving  E.  M.  F.  in  microvolts    .         .         .182 
Potential-series  of  metals  in  various  solutions         ....   216 
Specific  resistance  of  metals  and  alloys         .....   249 
Metals,  coefficient  for  calculating  change  of  resistance  with  tem- 
perature .         . 251 

Electrification,  change  in  apparent  resistance  of  insulators  due  to  .  255 
Insulators,  change  in  resistance  due. to  temperature  of  .  .  .  256 
Specific  resistance  of  bad  conductors  ......  258 

Specific  resistance  of  electrolytes 259 

Morse  Alphabet 299 

Arrival  curve,  table  of  ordinates  .         .  .         .         .         .  330 

Amplitude  of  dots  at  various  speeds     .         .         .         .         .         -331 

Wire  iron— sizes,  weights,  and  strengths 340 

Insulation  resistances  of  cables  per  knot        .....  346 


ELECTRICITY  AND   MAGNETISM, 


CHAPTER   I. 

ELECTRIC   QUANTITY. 

§  1.  A  PIECE  of  glass  and  a  piece  of  gutta  percha,  or  other 
resinous  material,  after  being  rubbed  together,  will  be  found 
to  attract  one  another  slightly.  One  piece  of  resin  thus 
rubbed  repels  another  similarly  treated  piece  of  resin,  and 
one  piece  of  rubbed  glass  repels  another  piece  of  rubbed 
glass ;  it  is  also  found  that  either  the  rubbed  resin  or  the 
rubbed  glass  attracts  any  light  body  in  its  neighbourhood. 
The  properties  acquired  by  the  glass  or  resin  are  not 
permanent. 

ELECTRICITY  is  the  name  given  to  the  supposed  agent 
producing  the  described  condition  of  bodies.  It  seems  to  have 
been  natural  to  regard  this  agent  as  a  kind  of  very  subtle 
fluid,  and  the  nomenclature  adopted  in  treating  of  electricity 
is  based  on  this  idea.  There  has  been  much  wrangling  as  to 
the  hypotheses  of  one  and  of  two  fluids.  It  is  quite  un- 
necessary to  assume  that  the  phenomena  are  due  to  one 
fluid,  two  fluids,  or  any  fluid  whatever ;  but  in  this  treatise 
the  names  employed  will  be  chiefly  those  which  have  been 
suggested  to  men  of  science  by  thinking  of  electrical  pheno- 
mena as  due  to  the  presence  or  absence  of  a  single  fluid. 

The  stick  of  resin  or  glass,  while  retaining  the  properties 


2  Electricity  and  Magnetism.  [CHAP.  1. 

described  above,  is  said  to  be  electrified  or  charged  with 
electricity  ;  it  carries  electricity  with  it  if  moved  from 
place  to  place.  If  these  electrified  bodies  are  wiped  with 
a  wet  cloth>  .a  damp  hand,  ^or  with  metal  foil,  they  cease  to 
be  electrifiecl^ ;  The  electricity  is  then  said  to  have  been 
conducted  .away  and,  the  bodies  which  allow  it  to  run  off  the 
glass  o.vVesm  ate  catied  coridaGtors  of  electricity.  Metals, 
water,  the  human  body,  damp  wood,  and  many  other  bodies 
are  conductors. 

The  air  must  be  a  non-conductor,  or  it  would  have  re- 
moved the  electricity  as  well  as  the  wet  cloth. 

Similarly,  the  resin  and  glass  themselves  are  non-con- 
ductors, for  when  the  electrified  pieces  are  simply  laid  on 
a  conductor  they  do  not  lose  all  their  electricity,  but  remain 
electrified  for  some  time  in  those  portions  which  are  not  in 
the  immediate  neighbourhood  of  the  conductor. 

Non-conductors  are  also  called  insulators.  Glass,  gutta 
percha,  india-rubber,  air,  are  examples  of  insulators. 

§  2.  If  a  small  piece  of  metal,  supported  by  an  insulating 
rod,  be  allowed  to  touch  the  electrified  piece  of  glass  or 
resin,  it  will  be  found  to  be  in  an  electrical  condition, 
similar  to  that  of  the  glass  or  resin  which  it  has  touched. 

The  insulated  conductor  which  has  touched  the  resin 
repels  the  resin  itself  or  any  other  insulated  conductor  which 
may  have  touched  the  electrified  resin  :  it  may  be  said  to 
be  electrified  as  the  resin  was,  or  charged  with  resinous 
electricity  ;  it  attracts  the  electrified  glass,  or  any  insulated 
conductor  electrified  by  the  glass  or  charged  with  what  is 
sometimes  called  vitreous  electricity. 

It  follows  from  these  experiments  that  part  of  the  elec- 
tricity on  the  resin  or  glass  is  communicated  to  any  conductor 
which  touches  either  of  the  bodies.  The  electrical  pro- 
perties gained  by  the  insulated  conductor  electrified  by 
contact  with  the  electrified  resin  have  been  gained  at  the 
expense  of  those  possessed  by  the  resin — the  resin  or  glass 
loses  what  the  metal  gains  ;  similarly,  the  electrified  con- 


CHAP.  I.]  Electric  Quantity.  3 

ductor  can  impart  a  portion  of  its  properties  to  another 
conductor,  losing  that  which  it  gives.  We  may,  then,  so  far 
as  can  be  yet  seen,  with  propriety  speak  of  a  conductor  as 
carrying  a  certain  quantity  of  electricity,  or  as  being  charged 
with  that  quantity. 

The  insulated  conductor  has  acquired  the  special  pro- 
perties in  virtue  of  which  the  resin  or  glass  was  said  to  be 
electrified,  or  charged  with  electricity;  but  the  insulated 
and  electrified  conductor  has  some  peculiarities  which  dis- 
tinguish it  from  a  similar  piece  of  an  electrified  insulator. 
For  instance,  if  the  conductor  be  touched  by  the  hand,  or 
by  the  point  of  a  wire  held  in  the  hand  of  a  man  not  him- 
self insulated,  it  will  lose  all  its  electricity  in  a  time  so  short 
as  to  appear  inappreciable ;  whereas  the  insulator  can  only 
lose  its  electricity  gradually,  when  every  part  of  its  surface 
has  been  successively  touched. 

We  may  also  expect  that  if  from  any  cause  the  distribu- 
tion of  electricity  in  a  body  can  be  varied,  even  without  its 
total  amount  being  changed,  this  redistribution  will  take 
place  almost  instantaneously  in  the  electrified  conductor, 
and  much  more  slowly  in  the  electrified  insulator. 

§  3.  The  force  exerted  (other  things  being  equal)  by  the 
electrified  body  on  another  similar  body  in  its  neighbour- 
hood, is  found  to  depend  on  the  quantity  of  electricity.  If 
I  halve  the  quantity,  distributing  that  electricity  over  two 
equal  balls,  which  was  previously  contained  on  one,  the 
force  exerted  by  the  electricity  on  each  ball  will,  under  any 
given  circumstances,  be  halved.  It  is  in  virtue  of  this  force 
only,  that  we  have  known  the  ball  to  be  electrified,  and  we 
may  therefore,  with  propriety,  speak  of  the  quantity  of 
electricity  on  each  ball  after  the  redistribution,  as  half  that 
on  the  first  ball  originally. 

Resin  and  glass  have  been  chosen  as  two  typical  materials, 
but  any  two  different  insulators  rubbed  together  behave  more 
or  less  as  resin  and  glass  do ;  thus  relatively  to  a  stick  of 
shellac  or  resin,  flannel  behaves  as  a  piece  of  glass  would  do. 


Electricity  and  Magnetism. 


[CHAP.  I. 


FIG.  i. 


§  4.  The  following  experiments  illustrate  what  precedes. 

Suspend  a  pith  ball  by 
a  silk  thread  (Fig.  i): 
pith,  in  order  that  the  ball 
may  be  light ;  silk,  in 
order  that  it  may  be  in- 
sulated.1 

1.  A    stick   of  shellac 
rubbed   with    flannel    at- 
tracts the  pith  ball. 

2.  After    contact    with 
the  shellac,  ihe  pith  ball 
will  by  conduction  become 
negatively    electrified    as 
the  shellac  is,  and  will  be 
repelled  by  it. 

3.  Arrange  the  flannel, 
which  is  not  a  very  good  insulator,  so  that  it  may  be  insulated 
both  while  rubbing  the  shellac,  and  afterwards ;  this  may  be 
done  by  shaping  it  like  a  cup,  and  supporting  it  on  a  silk 
thread,  or  by  gumming  it  on  a  metal  disc  fastened  to  a  stick 
of  vulcanite.     Then  the  flannel,  after  rubbing  the  shellac, 
will  be  electrified  with  vitreous   electricity,  and  will  attract 
the  pith  ball  electrified  with  resinous  electricity. 

Converse  effects  will  be  produced  by  electrifying  the  pith 
ball  by  means  of  the  flannel.  The  silk  threads,  shellac,  and 
flannel  must  all  be  very  dry,  or  the  moisture  will  form  a 
conductor  along  which  the  electricity  will  rapidly  escape. 
Sometimes  the  pith  ball  is  gilt,  to  make  it  a  better  conductor. 

Experiments,  illustrating  the  proportion  between  the  force 
observed  and  the  charge  of  electricity,  can  be  made  by 
means  of  the  pith  ball. 

4.  Two  pith  balls  electrified  with  different  electricities 
attract  one  another  (Fig.  2). 

1  The  parts  of  the  drawings  shown  dark,  but  crossed  by  thin  white 
lines,  are  intended  to  represent  insulators. 


CHAP,  i.]  Electric  Quantity.  5 

5.  Two  similarly  electrified  pith  balls  hung  side  by  side 
repel  one  another  (Fig.  3).  The  same  effect  may  be  observed 
by  means  of  two  pieces  of  gold  leaf  insulated,  and  hanging 
side  by  side.  When  these  apparatus  are  arranged  (as  in  Fig.  4) 

FIG.  2.  FIG.  3.  FIG.  4. 


with  glass  cases  and  stands,  and  with  means,  such  as  the 
metal  rod  a,  of  readily  communicating  an  electrical  charge 
from  any  body  the  condition  of  which  is  to  be  examined, 
they  are  called  electroscopes.1  They  indicate  the  presence 
of  electricity  by  showing  the  existence  of  a  force.  They 
do  not,  strictly  speaking,  measure  either  the  force  or  the 
quantity  of  electricity,  but  only  indicate  the  presence  of  some 
force  and  some  quantity.  The  little  electroscope  in  Fig.  4  is 
furnished  with  a  metal  cap  d,  and  two  uninsulated  strips  of 
metal  c  c,  the  object  of  which  is  explained  in  §  14  and  §  23. 
In  testing  the  laws  of  electrical  quantity,  it  is  convenient 
to  use  a  more  complex  arrangement  for  producing  electricity 
than  is  afforded  by  the  mere  stick  of  shellac  or  glass.  The 
common  electrical  machine  may  be  used  to  produce  the 
electricity.  This  machine  consists  of  a  plate  or  cylinder  of 
glass  rubbed  by  flannel  or  some  other  semi-insulator  while 
being  turned,  and  having  conductors  conveniently  arranged 
so  as  to  gather  either  the  vitreous  electricity  produced  on  the 
surface  of  the  glass  or  the  resinous  electricity  produced  on 
the  flannel.  The  best  construction  of  these  instruments  will 

1  The  name  electrometer  is  often  improperly  applied  to  what  is  above 
described  as  an  electroscope.     Electrometers  are  described  below,  §  18. 


6  Electricity  and  Magnetism.  [CHAP.  I. 

be  described  when  elec'.rical  laws  have  been  more  fully 
explained.  The  balls  by  which  the  foregoing  laws  are 
illustrated,  may  be  held  on  glass  or  vulcanite  stems,  which 
must,  however,  be  very  dry  and  clean,  or  the  electricity  will 
only  be  retained  for  a  very  short  time  upon  the  balls. 

§  5.  It  is  found  that  the  distribution  of  electricity  on 
the  balls  is  unaffected  by  the  mass  of  the  ball,  provided  the 
surface  remain  constant.  Balls  made  of  wholly  different 
materials  but  of  the  same  size,  if  their  surfaces  be  con- 
ductors, will  behave  in  a  precisely  similar  manner,  so  far  as 
regards  the  quantity  of  electricity  which  each  will  abstract 
from  any  electrified  body  which  it  may  touch  :  one  ball  may 
be  wholly  of  brass,  another  a  mere  gilded  pith  ball,  a 

FIG.  5. 


third  a  hollow  iron  ball;  yet  each  will  be  found  under 
similar  circumstances  to  have  what  may  be  termed  the  same 
capacity  for  electricity.  Moreover,  let  a  ball  (Fig.  5)  be  made 
of  two  hollow  hemispheres,  enclosing  an  independent  con- 
ducting ball  within  them,  and  in  contact  with  them,  and  let 
the  system  be  electrified  and  the  enclosing  hemispheres 
removed  by  insulating  handles.  The  internal  ball  will  not 
be  found  electrified,  and  the  two  hemispheres,  when  placed 
in  contact  so  as  to  form  a  complete  ball,  will,  if  the  insulation 
has  been  perfect,  be  found  to  be  as  strongly  electrified  as  at 
first.  Electricity,  while  at  rest,  is  therefore  looked  upon  as 
residing  in  the  surface  only  of  the  conductors.  These  state- 


CHAP,  I.]  Electric  Quantity.  7 

ments  may  be  verified  with  the  assistance  of  the  electro- 
scopes before  described. 

Although  electricity  when  at  rest  can  only  be  detected  on 
the  surface  of  bodies,  we  shall  presently  see  that,  when  in 
motion,  it  does  not  run  over  the  surface  only ;  it  will  pass 
more  readily  from  one  conductor  to  another  along  a  solid 
rod  than  along  a  hollow  rod  of  equal  external  dimensions 
and  the  same  materials,  vide  §  3,  Chapter  IV. 

§  6.  Let  one  insulated  conducting  ball  A  be  electrified  by 
contact  with  rubbed  resin,  and  another  exactly  similar  ball  B 
by  contact  with  rubbed  glass.  If  the  two  balls  be  now  put  in 
contact  with  one  another,  they  will  assume  an  electrical  condi- 
tion which  is  the  same  in  both.  If  the  ball  A  had  most  electri- 
city at  first,  the  whole  system  will  be  electrified  as  by  rubbed 
resin;  if  B  had  most  electricity  at  first,  the  whole  system 
will  be  electrified  as  by  rubbed  glass ;  and  in  all  cases  the 
quantity  of  electricity  on  the  two  balls  after  contact  will  be 
equal  to  the  difference  of  the  charge  on  the  two  balls  at  first 
(it  being  remembered  that  the  quantity  of  electricity  is 
assumed  to  be  measured  by  the  force,  which,  if  contained 
on  a  given  conductor,  it  would  be  capable  of  exerting). 

The  distinction  between  the  electricity  due  to  rubbed 
glass  and  that  due  to  rubbed  resin  is  therefore  analogous  to 
that  between  positive  and  negative  algebraic  quantities,  and 
justifies  the  use  of  the  epithets  positive  and  negative  in  place 
of  vitreous  and  resinous.  When  positive  and  negative 
electricities  are  summed,  the  result  is  equal  to  the  dif- 
ference between  the  arithmetical  values  of  the  quantities. 
If  the  two  quantities  of  electricity  of  different  kinds  were 
equal  on  the  two  balls,  the  result  of  the  contact  would  be 
wholly  to  put  an  end  to  all  electrical  charge.  The  two 
bodies  would  be  discharged  and  would  be  unelectrified, 
which  we  shall  find  to  mean  no  more  than  that  they  will  be 
in  the  same  condition  as  all  surrounding  uninsulated  bodies. 

§  7.  The  electricity  appearing  on  the  rubbed  glass  is 
called  positive,  that  appearing  on  the  rubbed  flannel  or 


8  Electricity  and  Magnetism.         (CHAP.  I. 

gutta  percha  is  called  negative;  and  the  algebraic  signs 
-f  and  —  are  often  used  to  denote  the  two  different  electrical 
conditions. 

-1-  positive,  vitreous  "I  are  three   synonymous   modes   of 

—  negative,  resinous  /  describing  electrical  conditions. 

The  symbols  +  and  —  have  already  been  used  on  the 
foregoing  figures  showing  attractions  and  repulsions,  + 
repels  +  ;  —  repels  —  ;  +  attracts  — . 

§  8.  When  electricity  is  produced,  it  is  found  invariably 
that  equal  quantities  of  positive  and  negative  electricity  are 
produced.  True,  the  glass  when  rubbed  becomes  positive 
only,  but  the  material  with  which  it  is  rubbed  becomes 
negative,  and  the  quantity  on  the  glass  is  precisely  equal 
and  opposite  to  that  upon  the  rubber.  If  the  rubber  be  not 
insulated,  the  electricity  upon  it  will  be  at  once  conducted 
to  the  earth,  and  will  for  the  time  being  make  the  rest  of 
the  earth  more  negative  than  before  ;  but  the  earth,  including 
the  rubbed  piece  of  glass,  contains  as  a  whole  neither  more 
nor  less  electricity  than  it  did  before  ;  the  distribution  only 
has  been  altered. 

When  the  whole  surfaces  of  the  two  substances  which 
have  been  rubbed  together  are  thoroughly  connected,  either 
through  the  intervention  of  the  mass  of  the  earth  or  by 
any  other  conductor,  the  positive  and  negative  electricities 
disappear,  being  neutralised  as  before.  No  substance  is  found 
to  insulate  so  perfectly  as  to  possess  the  power  of  keeping 
the  two  electricities  asunder  for  more  than  a  limited  time.  A 
perpetual  leakage  is  always  occurring  from  the  one  to  the  other 
through  the  mass  of  the  insulator,  until  the  combination  or 
neutralisation  is  complete  and  all  signs  of  electricity  dis- 
appear. In  elementary  electrical  experiments  the  one  kind 
of  electricity  only  is  made  manifest,  because  the  one  kind  is 
concentrated  in  a  small  conductor  and  the  other  is  probably 
diffused  over  the  earth  in  the  neighbourhood  ;  the  quantity 
at  any  one  spot  being  too  small  to  produce  appreciable 
effects.  Thus,  when  a  stick  of  sealing-wax  (being  one  kind 


CHAP.  I.]  Electric  Quantity.  9 

of  resin)  is  rubbed  by  a  doth,  the  sealing-wax  alone  appears 
electrified,  simply  because  the  positive  electricity  diffuses 
itself  over  the  earth  from  the  cloth,  through  the  hand  of 
the  person  holding  it. 

§  9.  When  one  insulator  is  rubbed  against  another,  one 
of  them  becomes  charged  with  positive  and  the  other  with 
negative  electricity ;  and  with  any  given  pair  of  materials, 
one  invariably  becomes  positively  and  the  other  negatively 
electrified;  but  whereas  glass  rubbed  with  silk  or  flannel 
becomes  positively  electrified,  when  rubbed  with  a  cat's  skin 
it  becomes  negatively  electrified.  It  follows  from  this  that 
the  positive  or  negative  electrification  of  the  material  does 
not  depend  absolutely  on  the  substance  of  that  material, 
but  depends  on  some  peculiar  relation  between  the  two 
substances  in  contact  It  is  proved  by  experiments  that  all 
insulators  can  be  arranged  as  in  the  following  list,  which  is 
such  that  those  first  on  the  list  invariably  become  positive 
when  rubbed  by  any  of  the  substances  taking  rank  after 
them,  but  negative  when  rubbed  by  a  substance  preceding 
them.  This  list  is  given  on  the  authority  of  M.  Ganot. 

Cat's  skin.  Flannel. 

Glass.  Cotton. 

Ivory.  Shellac. 

Silk.  Caoutchouc. 

Rock  crystal.  Resin. 

The  hand.  Gutta  percha. 

Wood.  Metals. 

Sulphur.  Gun  cotton. 

Those  bodies  which  stand  far  apart  on  the  list  are  dis- 
tinctly and  decidedly  positive  or  negative  relatively  to  one 
another,  but  those  bodies  which  appear  near  together  on  the 
list  may  possibly  be  misplaced.  A  very  trifling  difference  in 
the  composition  of  the  body,  or  even  in  the  state  of  its  surface 
or  of  the  colouring  matter  employed,  will  raise  or  lower  the 
place  of  the  body  in  the  list.  A  rise  in  temperature  lowers  the 
body  in  the  list,  i.e.  a  hot  body  rubbed  by  a  cold  one  identical 


IO  Electricity  and  Magnetism.  [CHAP.  I. 

with  it  in  chemical  composition  becomes  negatively  elec- 
trified. Generally  it  may  be  said  that  no  difference  between 
two  insulators  can  be  so  trifling  as  not  to  necessitate  the 
production  of  electricity  when  they  are  rubbed  together. 
The  relative  position  of  two  bodies  on  the  scale  can  be 
readily  tested  by  rubbing  two  insulated  discs  together  and 
observing  their  action  on  a  pith  ball  charged  with  electricity 
of  a  known  character  or  sign. 

§  10.  The  word  potential  will  now  be  substituted  for  the 
general  and  vague  term  electrical  condition.  When  a  body 
charged  with  positive  electricity  is  connected  with  the  earth 
electricity  is  transferred  from  the  charged  body  to  the  earth  ; 
and,  similarly,  when  a  body  charged  with  negative  elec- 
tricity is  connected  with  the  earth  electricity  is  transferred 
from  the  earth  to  the  body.  Generally,  whenever  two 
conductors  in  different  electrical  conditions  are  put  in  con- 
tact electricity  will  flow  from  one  to  the  other.  That  which 
determines  the  direction  of  the  transfer  is  the  relative 
potential  of  the  two  conductors.  Electricity  always  flows 
from  a  body  at  higher  potential  to  one  at  lower  potential 
when  the  two  are  in  contact  or  connected  by  a  conductor. 
When  no  transfer  of  electricity  takes  place  under  these  con- 
ditions the  bodies  are  said  to  be  at  the  same  potential,  which 
may  be  either  high  or  low.  The  potential  of  the  earth  is 
assumed  as  zero.  The  potential  of  a  body  is  the  difference 
of  its  potential  from  that  of  the  earth.  Potential  admits  of 
being  measured  and  this  measurement  is  fully  described  with 
the  conditions  -tending  to  produce  a  given  potential  in 
Chapter  II.  Difference  of  potential  for  electricity  is  ana- 
logous to  difference  of  level  for  water.  From  the  above 
definition  it  follows,  that  all  parts  internal  and  external  of 
any  conductor  in  or  on  which  electricity  is  at  rest  must  be  at 
one  potential. 

A  body  is  said  to  be  uninsulated  when  connected  by  a 
conductor  with  the  earth.  The  potential  of  any  uninsulated 
body  is  neither  negative  nor  positive.  There  is  in  this 


CHAP.  L]  Electric  Quantity.  1 1 

view  nothing  to  prevent  our  regarding  the  earth  as  an  electri- 
fied body;  indeed,  we  know  that  any  one  part  of  the  earth 
is  seldom  or  never  in  exactly  the  same  electrical  condition 
as  any  other  part  in  the  neighbourhood.  We  simply  assume 
as  our  zero  the  condition  of  the  earth  in  our  neighbourhood 
for  the  time  being;  just  as  we  may  assume,  in  measuring 
heights,  any  arbitrary  level,  such  as  Trinity  high- water  mark: 
a  point  above  this  is  a  positive  height,  a  depth  below  it  may 
be  written  or  regarded  as  a  negative  height. 

§  11.  It  is  frequently  said  that  positive  electricity  attracts 
negative  electricity,  but  that  positive  repels  positive  and 
negative  repels  negative.  We  have  stated  that  electrified 
bodies  do  present  attractions  and  repulsions  of  this  kind, 
and  by  a  slight  extension  of  language  the  electricity  itself 
may  be  spoken  of  as  attracting  or  repelling ;  but  there  is  a 
further  phenomenon  called  statical  induction,  which  does 
appear  more  distinctly  to  represent  an  attraction  or  repulsion 
of  electricity,  besides  the  attraction  and  repulsion  of  the 
bodies  charged  with  electricity.  A  body  A  brought  into 
the  neighbourhood  of  a  body  B  at  a  different  potential 
immediately  produces  a  distribution  of  electricity  over  the 
surface  of  B,  such  as  would  be  produced  by  the  system  of 
attractions  and  repulsions  enumerated  in  §  7.  If  A  be 
charged  positively  it  attracts  negative  electricity  to  that  end 
of  the  body  B  which  is  near  it,  and  repels  positive  electricity 
to  the  remoter  portions  of  B.  If  the  body  B  be  insulated, 
it  neither  loses  nor  gains  electricity,  but  its  ends  are  com- 
petent to  produce  electrical  phenomena  of  opposite  kinds. 
Separating  the  two  ends  we  may  retain  each  charged  with 
its  positive  and  negative  electricity.  Or  if  we  connect  the 
further  end  of  B  with  the  earth  even  for  a  moment,  the 
positive  electricity  will  be  driven  off  to  the  earth,  and  a 
permanent  negative  charge  will  then  be  retained  on  B, 
Otherwise  when  A  is  removed  the  +  and  —  electricities  on 
B  recombine  and  exactly  neutralise  one  another.  By  in- 
duction, as  in  the  case  of  electricity  obtained  by  friction, 


12 


Electricity  and  Magnetism. 


[CHAP.   I. 


precisely  equal  quantities  of  positive  and  negative  elec- 
tricities are  simultaneously  produced.  It  will  be  convenient 
to  represent  the  distribution  of  electricity  on  the  surface 
of  bodies  by  dotted  lines,  the  distances  of  which  from 
the  surface  are  proportional  to  the  quantity  of  electricity 
per  square  inch  at  that  point ;  then,  if  the  electricity  be 
positive  the  dotted  line  will  be  shown  outside  the  body ; 
if  negative,  the  dotted  line  will  appear  inside  the  body. 
Along  one  line  separating  the  positively  charged  portion 
from  the  negatively  charged  portion  there  will  be  absolutely 
no  charge.  The  annexed  Figure  (6)  represents  an  original 
and  an  induced  charge  represented  to  the  eye  according  to 
this  plan.  The  dotted  line  on  A  shows  the  original  charge 

FIG.  6. 


when  A  was  at  a  great  distance  from  B.  When  brought  into 
the  position  A]  near  B  the  original  distribution  is  disturbed, 
and  at  the  same  time  positive  and  negative  electricities  are 
induced  at  the  two  ends  of  B  ;  at  the  point  e  there  is  no 
charge. 

§  12.  This  induction  of  electricity  must  take  place  in  the 
space  surrounding  every  electrified  body.  In  a  room  con- 
taining a  ball  electrified  positively,  the  surface  of  the  walls,  the 
furniture,  the  experimenter  himself  must  necessarily  all  be 
charged  negatively  in  virtue  of  this  induction.  Where  does 
this  negative  electricity  come  from  ?  If  the  electrified  body 
has  been  charged  positively  by  rubbing,  and  the  negative 
electricity  has  been  allowed  free  access  to  the  earth,  it  may 


CHAP.  I.]  Electric  Quantity.  13 

be  said  that  this  negative  electricity  has  been  attracted  to 
the  surface  of  the  walls,  furniture,  &c.,  distributing  itself 
according  to  definite  laws  which  must  be  separately  studied. 
If  both  rubber  and  glass  have  been  insulated,  then  each 
induces  on  all  surrounding  surfaces  positive  and  negative 
electricities  equal  each  to  each,  but  these  induced  quantities 
are  now  not  necessarily  equal  to  the  amount  on  the  glass 
or  on  the  rubber,  unless  these  be  removed  very  far  apart 
from  one  another.  If  the  two  oppositely  electrified  bodies 
are  kept  close  together,  their  inductive  actions  are  spent 
almost  entirely  on  each  other  and  their  action  on  the 
surrounding  walls  of  the  room  is  almost,  nothing,  for 
where  the  one  tends  to  induce  a  positive,  the  other  tends 
to  induce  a  negative  charge;  as  the  insulated  electrified 
bodies  are  removed  farther  apart  each  produces  its  in- 
dependent effect  more  completely.  It  will  be  found  im- 
possible rightly  to  understand  electrical  phenomena  without 
always  recognising  the  presence  of  this  induced  charge  of 
electricity  opposite  in  character  to  the  first  or  original  charge. 
The  very  existence  of  the  original  charge  implies  the  induced 
charge. 

§  13.  Induction  always  takes  place  between  two  con- 
ductors at  different  potentials  separated  by  an  insulator.  If 
the  conductors  are  at  the  same  potential,  whether  this  be 
high  or  low,  there  is  no  induction. 

If  the  wall  of  the  room  and  an  insulated  body  inside 
the  room  are  at  the  same  potential,  the  insulated  body 
will  be  found  to  produce  no  electrical  effects.  The  walls 
of  the  room  and  the  insulated  body  might  both  be  insu- 
lated from  the  earth  and  at  a  high  potential,  but  none  of 
the  electrical  effects  hitherto  described  could  be  produced 
by  an  experimenter  in  the  room.  The  insulated  body  would 
not  attract  light  bodies;  it  would  induce  no  charge  or  redis- 
tribution of  electricity  on  a  conductor  held  in  its  neigh- 
bourhood, and  would  not  itself  be  charged  with  -electricity 
or  electrified.  To  produce  all  these  phenomena  we  require 


14  Electricity  and  Magnetism.  [CHAP.  i. 

not  only  that  the  insulated  body  in  the  room  be  at  a  high 
potential,  but  that  the  surrounding  walls  be  at  a  different 
potential.  If  the  insulated  body  at  a  high  potential  were 
connected  with  the  earth  electricity  would  run  from  it  to  the 
earth,  and  then  a  negative  charge  would  appear  on  the 
surface  of  the  body  and  a  positive  charge  on  the  inside  of 
the  room.  The  body  would  then  become  electrified. 

§  14.  Viewed  in  the  light  given  by  these  facts  the  attrac- 
tion which  an  electrified  body  A  exerts  on  uncharged  bodies 
in  the  neighbourhood  is  simply  due  to  the  induced  elec- 
trification which  it  produces  in  those  bodies.  The  light 
uninsulated  body  B  (Fig.  7)  is  attracted  to  the  negatively 


FIG. 


FIG.  8. 


electrified  body  A  in  virtue  of  the  positive  charge  on  B  ;  this 
positive  charge  is  also  repelled  by  the  walls  of  the  room 
which  will  be  positively  electrified  by  induction  from  A. 
The  light  insulated  body  B  (Fig.  8)  is  attracted  because  its 
charge  at  the  near  Side  is  attracted.  The  charge  on  the 
far  side  of  B  is  repelled,  on  the  contrary,  by  the  body  A, 
but  less  repelled  than  the  near  side  is  attracted,  because  it 
is  more  distant.  The  charge  on  the  near  side  of  B  is  again 
repelled  from  the  walls  of  the  room  towards  the  body  A  ; 
the  charge  on  the  far  side  is  attracted  towards  the  walls 
and  from  A,  but  less  than  the  near  side  is  attracted,  because 
the  far  side  is  nearer  the  walls.  It  is  not  until  all  these 


CHAP.  I.]  Electric  Quantity.  \  5 

actions  are  taken  into  account  that  the  forces  set  in  action 
can  be  fully  calculated ;  moreover,  unless  B  be  very  small, 
it  disturbs  the  distribution  of  electricity  on  A  very  sensibly. 

In  the  electroscope  shown  in  Fig.  4,  §  3,  the  metal  strips  cc 
are  inductively  electrified  by  any  charge  on  the  gold  leaves 
bb.  They  attract  the  gold  leaves  and  increase  their  diver- 
gence. They  also  make  the  action  of  the  instrument  more 
regular  than  it  could  be  if  glass  were  opposite  b  b,  for 
the  glass  would  always  be  liable  to  have  an  electrical  charge 
of  its  own,  independently  of  any  charge  on  bb. 

A  similar  complicated  series  of  actions  occur  when  a 
positively  electrified  ball  is  brought  into  the  neighbourhood 
of  another  positively  electrified  ball  :  each  ball  repels  its 
neighbour  and  is  attracted  by  the  negative  induced  electri- 
city on  the  surrounding  walls.  If  the  walls  were  positive 
also  they  would  repel  the  balls  back  to  one  another,  and  if  all 
were  at  the  same  potential  the  two  positive  balls  would  be  in 
equilibrium  and  would  not  be  electrified. 

The  phenomenon  of  induction  allows  us  to  examine  the 
electrical  condition  of  any  body  without  abstracting  elec- 
tricity from  it.  If  I  hold  a  positively  electrified  body  over 
the  knob  on  the  electroscope  (Fig.  4),  the  knob  will  be 
negatively  charged  and  the  gold  leaves  positively  charged 
by  induction  ;  the  gold  leaves  will  therefore  be  deflected. 
On  the  removal  of  the  inducing  body,  the  electricities  re- 
combine  and  the  deflection  ceases.  It  is  easy,  however,  by 
touching  the  under  side  of  the  knob  or  plate  used  for  this 
purpose  with  an  uninsulated  conductor  such  as  the  hand,  to 
allow  the  one  electricity  to  run  to  earth,  and  then  we  have 
the  electroscope  permanently  charged  with  electricity  of 
the  opposite  kind  to  that  contained  on  the  inducing  body. 

§  15.  The  distribution  of  electricity  can  be  examined  in 
two  ways,  the  first  of  which  is  the  following.  We  may 
touch  the  surface  of  the  body  which  we  believe  to  be 
electrified  with  a  small  insulated  disc  called  a  proof  plane, 
and  then  remove  this  conductor,  and  observe  whether  it  is 


1 6  Electricity  and  Magnetism.          [CHAP.  I. 

competent  to  produce  any  of  the  electrical  attractions  and 
repulsions  or  inductions.  If  the  conductor  be  small,  and 
if  it  be  held  on  a  long  insulating  stem  of  small  size  also, 
it  will  not  much  disturb  the  distribution  of  the  electricity 
over  the  surface  to  be  tested  though  some  disturbance  will 
always  be  produced  by  induction.  While  touching  the 
body,  it  will  sensibly  form  part  of  the  surface  of  that  body, 
and  will  be  charged  as  the  body  is  charged  at  that  point,  or 
nearly  so.  When  removed,  it  will  therefore  retain  a  charge 
nearly  proportional  to  what  is  termed 
the  density  of  the  electricity  at  that 
point,  and  this  density  may  therefore 
be  tested  by  observing  the  attracting  or 
repelling  force  which  the  proof  plane 
is  in  each  case  capable  of  exerting 
directly  or  by  induction  on  some  body 
assumed  to  be  at  a  constant  electrical 
potential  —  for  instance,  on  the  pith 
ball  electroscope.  By  experiments  of 
this  nature,  the  distribution  of  electri- 
city has  been  studied,  and  it  is  found 
that  no  electricity  can  be  detected  inside 
a  hollow  and  empty  conductor.  A  proof 
plane  introduced  (as  in  Fig.  9)  into  the 
interior  of  a  highly  electrified  ball  with- 
draws no  sensible  charge  of  electricity 
unless  by  accident  it  touches  the  edge  of  the  aperture  while 
being  withdrawn.  This  distribution  is  a  necessary  conse- 
quence of  the  law  that  each  elementary  portion  of  a  charge 
of  electricity  repels  every  other  similar  portion  with  a  force 
inversely  proportional  to  the  square  of  the  distance  separat- 
ing them.  We  shall  study  hereafter  a  few  of  the  laws  of 
distribution  of  electricity  on  the  surface  of  conductors  of 
regular  form,  on  the  assumption  that  they  are  so  far  from 
all  neighbouring  conductors,  that  the  distribution  depends 
only  on  the  form  of  the  electrified  surface.  These  laws 


CHAP.  I.j  Electric  Quantity.  17 

will  show  that  electricity  tends  to  accumulate  on  all  pro- 
jections, and  that  the  density  at  points  is  necessarily  very 
large.  Next  we  must  study  the  distribution  of  electricity 
over  two  conducting  surfaces  opposite  each  other.  The 
distribution  in  this  case  depends  not  only  on  the  form  of 
each  surface,  but  on  their  proximity.  For  instance,  the 
inside  of  a  hollow  conductor  will  be  inductively  charged 
by  any  electrified  and  insulated  body  placed  there,  and  the 
charge  on  the  internal  surface  will  be  greater  the  closer  the 
two  surfaces  are  placed.  The  charge  is  also  affected  by 
the  insulator  separating  the  conductor. 

A  second  mode  of  testing  the  distribution  of  electri- 
city is  to  remove  the  portion  of  the  body  the  electricity  of 
which  is  to  be  tested  from  the  system  of  which  it  forms  part, 
by  insulating  it  from  that  system  ;  its  electricity  may  then 
be  tested  by  the  proof  plane  or  by  its  direct  effects. 

§  16.  It  follows  from  what  has  already  been  stated  (§  n) 
that  an  electrified  conductor  may  at  certain  portions  of  its 
surface  have  little  or  no  charge.  If  those  parts  are  touched 
by  the  proof  plane  no  electricity  will  be  removed  by  it. 
Thus,  if  a  cylinder  be  electrified  by  induction,  so  that  one 
end  is  positive,  the  other  end  negative,  as  shown  on  the 
body  B,  Fig.  6,  some  point  near  the  middle  at  e  will  not  be 
charged.  It  will  not  electrify  the  proof  plane  or  any  other 
small  conductor,  and  even  if  a  portion  of  the  cylinder  itself 
be  removed  it  will  give  no  signs  of  electricity.  If  it  be 
touched  by  a  large  conductor,  the  whole  distribution  of 
electricity  will  be  changed  by  induction  before  the  contact 
takes  place.  Thus,  if  I  connect  the  point  e,  Fig.  6,  with 
the  earth  the  whole  distribution  of  electricity  on  B  will  be 
changed,  for  although  e  is  no  more  charged  with  electricity 
than  the  earth  itself  the  potential  of  the  whole  body  B  has 
been  raised  by  induction  from  A  on  B  ;  the  approach  of 
the  connecting  wire  alters  the  distribution  of  electricity, 
positive  electricity  accumulates  opposite  the  wire  even  be- 
fore the  contact  is  made,  and  the  result  of  connecting  e  with 

c 


1 8  Electricity  and  Magnetism.  [CHAP.  i. 

the  earth  would  be  to  leave  the  body  B  charged  with  negative 
electricity  only  and  at  the  potential  of  the  earth. 

There  are  distributions  of  electricity  such  that  the  electri- 
fied conductor  may  actually  be  in  contact  with  the  largest 
conductor  or  with  the  earth  without  losing  its  electricity  or 
the  distribution  being  in  any  way  changed,  the  conductor 
being  at  the  potential  of  the  earth ;  for  instance,  consider  the 
positively  electrified  conductor  A,  Fig.  10,  insulated  and 
separated  from  the  conductor  B  by  a  thin  dielectric  c.  Let 
there  be  a  negative  charge  on  the  conductor  B.  equal  to  the 
positive  charge  on  A,  then  no  sensible  charge  will  be  found 
upon  the  external  surface  of  either  A  or  B,  supposing  them 
held  far  away  from  other  conductors.  I  can  produce  this 
distribution  by  electrifying  A  while  B  is  in  contact  with  the 
earth.  The  positive  charge  on  A  will  induce  a  negativ6 
charge  on  B,  as  shown  by  the  dotted  lines.  The  charge 
on  A  will  be  on  the  surface  opposite  B  :  the  charge 
on  B  will  be  on  the  surface  opposite  A.  I  may  then 
allow  either  A  or  B  to  be  in  connection  with  the  earth 
without  sensibly  disturbing  the  charge  on  A  or  B.  If  I 
allow  both  to  be  in  connection  with  the  earth  or  with  one 
another,  the  electricities  will  combine  and  neutralise  one 
another.  The  dielectric  need  not  be  solid,  as  in  Fig.  10, 
but  may  consist  of  air  only,  as  in  Fig.  n.  The  distri- 
bution of  electricity  described  is  that  which  occurs  in 
a  charged  Leyden  jar  (Fig.  1 2).  The  outside  coating  A  has 
a  large  charge  of  electricity  almost  equal  to  the  charge  of 
the  internal  coating  B  ;  nevertheless  none  of  the  electricity 
runs  from  the  outer  coating  to  the  earth.  The  potential 
of  the  outer  coating  is  zero.  It  is  often  said  that  electricity 
in  this  case  is  latent  or  fixed — in  truth  it  is  no  more  latent 
or  fixed  than  any  other  charge  of  electricity.  The  distribu- 
tion in  this  case  is  such  that  no  sensible  charge  is  on  the 
outside  of  the  outside  coating,  the  whole  quantity  being  on 
the  inside  of  the  outside  coating. 

If  we  were  to  form  a  Leyden  jar  with  an  opening  ad- 


CHAP.  I.] 


Electric  Quantity. 


mitting  the  introduction  of  a  proof  plane  between  the  inner 
and  outer  coatings,  we  might  take  off  from  either  coating  a 
quantity  proportional  to  the  charge  at  each  place.  This,  in 
fact,  is  what  we  do  when  by  the  proof  plane  we  remove  a 
portion  of  the  charge  from  a  conductor  inside  a  room,  or 
from  the  walls  of  a  room  inside  which  an  electrified  body  is 


FIG.  10. 


FIG.  i2. 


FIG.  ii. 


placed.  There  is  no  difference  in  theory  between  the  inner 
and  outer  coatings  of  the  Leyden  jar ;  the  outside  of  the 
inner  coating,  the  inside  of  the  outer  coating  are  charged. 
From  these  electricity  can  be  withdrawn  by  the  proof 
plane ;  from  the  other  faces  of  either  coating  none  can  be 
taken. 

Whenever  a  conductor  is  charged  a  kind  of  Leyden  jar  is 
necessarily  formed.  The  conductor  is  the  inner  coating, 
the  air  the  dielectric,  and  the  nearest  surrounding  conductors, 
such  as  the  wall  of  the  room  or  the  person  of  the  operator, 
form  the  outer  coating;  but  the  name  of  'Leyden  jar'  is 
reserved  for  those  cases  in  which  the  two  opposed  con- 
ductors are  brought  very  close  together  purposely.  The 


2O  Electricity  and  Magnetism.  [CHAP.  T. 

arrangement  is  also  called  a  condenser  or  accumulator.  The 
difference  of  potential  between  the  two  coatings  of  the 
Leyden  jar  remains  constant  whichever  coating  is  in  connec- 
tion with  the  earth.  If  the  original  charge  on  the  inside  be 
positive,  the  outer  insulated  coating  will  be  at  a  negative 
potential  when  the  inner  coating  is  put  to  earth. 

§  17.  The  quantity  of  electricity  on  a  given  conductor 
may  be  measured.  The  existence  of  the  quantity  of  elec- 
tricity is  proved  merely  by  the  force  which  it  exerts  on  other 
quantities  of  electricity.  In  order  to  measure  quantities  of 
electricity  we  must  therefore  measure  the  relative  forces 
which  different  quantities  exert  under  the  same  circum- 
stances :  if  a  quantity  A  of  electricity  exerts  twice  the  force 
that  quantity  B  exerts  under  precisely  similar  circumstances, 
we  may  properly  say  that  quantity  A  is  double  the  quantity 
B.  In  order  to  measure  anything  a  unit  must  be  adopted. 

The  unit  quantity  .of  electricity  may  conveniently   be 
called   that    quantity   which,   concentrated   at   one   point, 
would  exert  the  unit  force  upon  a  similar  and  equal  quantity 
concentrated  at  a  point  distant  by  one  unit  of  length.  There 
are  many  different  units  of  length  and  force  which  might  be 
adopted.     The  units  chosen  by  the  author  in  the  present 
work  are  the   centimetre  for  the  measure  of  length  ;    and 
the  force  capable   of  giving  in  one  second  a  velocity  of 
one  centimetre  per  second  to  a  gramme  mass  for  the  unit 
of  force.     The  unit  quantity  of  electricity  upon  this  system, 
known  as  the  electro- static  system,  is  that  which  if  concen- 
trated at  one  point  would  repel  an  equal  quantity  at  a  point 
one  centimetre  distant  with  such  a  force  as  would,  after 
acting  for  one  second,   cause  a   gramme  to  move  with  a 
velocity  of  one  centimetre  per  second.      Another  unit  of 
electricity  might  be  defined  as  that  which  would  repel  a 
similar  unit  with  the  force  of  one  grain  at  a  distance  of  one 
foot.     The  idea  at  the  root  of  both  definitions  would  be 
identical,  but  the  apparently  more  complex  definition  leads 
to  greater  simplicity  in  calculations. 


CHAP.  I.]  Electric  Quantity.  21 

§  18.  The  practical  measurement  of  quantities  of  electri-. 
city  can  in  many  cases  be  made  by  directly  measuring  the 
electrical  forces  in  action;  the  apparatus  in  which  these 
forces  are  weighed  is  called  an  absolute  electrometer.  Any 
apparatus  in  which  the  forces  produced  by  different  quantities 
under  the  same  circumstances  are  numerically  compared  but 
not  actually  measured  in  units  of  force  is  termed  an  electro- 
meter. Indirect  methods  of  measuring  quantity  are  often 
more  convenient  for  practical  purposes,  but  these  measure- 
ments can  and  ought  to  be  all  made  in  units  of  the  kind 
described.  In  studying  the  distribution  of  electricity  under 
various  conditions,  we  must  not  be  satisfied  with  merely 
knowing  generally  that  at  certain  points  there  will  be  more, 
at  others  less,  electricity;  we  must  not  even  be  satisfied 
with  knowing  the  relative  amounts  on  various  points  of  a 
given  conductor ;  we  must  aim  at  knowing  exactly  the 
quantity  of  electricity  per  square  unit  of  surface,  which  is 
termed  the  density  of  the  electrical  charge.  The  electro- 
meters employed  in  comparing  quantities  of  electricity  on 
different  portions  of  any  surface  or  surfaces  must  give  us 
the  relative  amounts  on  various  points,  or  they  will  not  be 
measuring  instruments.  An  absolute  electrometer  does  more, 
it  gives  not  only  the  relative  but  the  absolute  amounts. 

§  19.  Hitherto  electricity  has  been  spoken  of  as  pro- 
duced directly  by  friction  and  indirectly  by  statical  induc- 
tion only;  there  are  several  other  modes  by  which  elec- 
tricity is  produced  : — i.  The  simple  contact  of  two  in- 
sulated pieces  of  dissimilar  metals  results  in  charging  one 
metal  with  positive,  the  other  with  negative  electricity  in 
precisely  equal  amounts ;  or  it  may  be  more  correct  to  say 
that  after  contact  the  metals  are  found  to  be  thus  dissimilarly 
charged.  The  charges  so  produced  or  observed  are  very 
small.  2.  If  a  metal  be  dipped  in  a  liquid  a  similar 
effect  occurs,  the  liquid  and  the  metal'  being  electrified  in 
opposite  ways.  A  difference  of  potentials  is  produced  by 
the  contact.  The  amount  of  electrification  differs  with 


22 


Electricity  and  Magnetism.  [CHAP.  I. 


different  metals  and  different  liquids,  but  is  always  very 
small  compared  with  that  which  might  be  produced  by 
friction.  3.  When  two  dissimilar  metals  are  plunged  side 
by  side  into  a  liquid,  such  as  water  or  a  weak  solution  of 
sulphuric  acid,  they  do  not  exhibit  any  signs  of  electrification. 
The  three  materials  remain  at  one  potential  or  nearly  so.1 
A  further  description  of  this  curious  fact  is  given  Chapter  II. 
§  22.  4.  If  while  the  two  dissimilar  metals  are  in  the 
liquid  they  are  joined  by  metallic  contact  to  terminal  pieces 
of  one  and  the  same  metal,  these  terminal  pieces  will  be 
brought  to  the  same  difference  of  potentials  as  that  which 
would  be  produced  by  direct  contact  between  the  dissimilar 
.metals.  Thus,  though  zinc,  water,  and  copper  in  an  insulated 

FIG.  13. 


jar  are  all  at  one  potential,  if  I  join  a  copper  terminal  10  the 
zinc,  then  this  copper  terminal  will  become  positive  rela- 
tively to  the  zinc,  water,  and  second  copper,  which  all  remain 
at  one  potential. 

The  name  of  galvanic  cell  is  given  to  an  insulating  jar  con- 
taining two  dissimilar  metals  plunged  in  a  liquid  composed 
of  two  or  more  chemical  elements,  one  of  which  at  least 
tends  to  combine  with  one  or  other  of  the  two  metals,  or 

1  The  Voltaic  theory  of  the  galvanic  cell  is  adopted  in  this  treatise. 
The  above  statement  is  in  direct  contradiction  with  many  treatises  on 
electricity,  which  generally  state  that  the  metals  become  one  positive, 
and  the  other  negative.  Vide  Chapter  TT.  §  23. 


CHAP.  I.]  Electric  Quantity.  23 

both  in  different  degrees.  But  whereas  in  the  single  cell  no 
charge  of  electricity  is  given  to  either  metal,  if  we  insulate 
successive  jars  of  the  liquid  one  from  another,  and  plunge 
successive  pairs  of  metals,  c  and  z,  joined  as  in  Fig.  13, 
into  these  jars,  very  considerable  charges  of  electricity  will 
be  communicated  to  conductors  in  contact  with  the  final 
plates  of  metal ;  thus,  if  coppers  and  zincs  be  used,  the 
liquid  being  water  or  a  weak  solution  of  sulphuric  acid,  the 
last  copper  plate  will  charge  a  conductor  positively,  the 
last  zinc  plate  an  equal  conductor  negatively.  Sulphate 
of  zinc  will  be  formed  during  the  process,  and  this  'chemical 
action  is  found  to  be  essential  to  the  production  of  any 
considerable  quantity  of  electricity  in  this  manner,  which  is 
therefore  often  said  to  be  due  to  chemical  action  as  dis- 
tinguished from  friction.  The  charge  of  electricity  obtained 
in  this  way  may  be  looked  upon  as  wholly  due  to  the 
chemical  action ;  but,  on  the  other  hand,  it  may  be  looked 
upon  as  due  to  the  successive  junctions  between  the  zincs 
and  coppers,  and  it  is  found  that  the  amount. of  charge 
obtained  in  this  manner  on  a  given  conductor  is  simply 
proportional  to  the  number  of  these  junctions,  and  that  it 
depends  on  the  metals  in  contact,  not  upon  the  liquids. 
In  other  words,  the  difference  of  potentials  produced  is 
proportional  to  the  number  of  junctions.  These  two  views 
are  called  respectively  the  chemical  theory  and  the  contact 
theory  of  the  galvanic  cell,  and  have  been  supposed  to  be 
incompatible.  They  are  both  true. 

§  20.  There  is  no  difference  whatever  in  kind  between 
the  electricity  produced  by  friction  and  that  produced  by 
chemical  reaction.  It  is  worthy  of  remark  that,  in  each 
case,  the  electricity  requires  for  its  production  the  contact  of 
dissimilar  materials.  This  contact  requires  to  be  supple- 
mented by  friction  in  the  case  of  insulators,  by  chemical 
reaction  in  the  case  of  conductors.  The  friction  between 
two  dissimilar  insulators  invariably  produces  electricity.  The 
difference  of  the  chemical  action  of  any  conducting  liquid 


24  Electricity  and  Magnetism.  [CHAP.  I. 

compound  on  two  dissimilar  rnetals  produces  electricity. 
The  analogy  between  friction  and  chemical  action  is  not 
known.  Electricity  in  each  case  is  produced  so  that  equal 
quantities  of  positive  and  negative  electricity  are  simulta- 
neously produced.  This  is  sometimes  expressed  by  saying 
that  all  bodies  are  always  electrified,  and  that  the  contact 
and  friction,  or  contact  and  chemical  action,  produce 
merely  a  redistribution  of  electricity. 

§  21.  Electricity  may  also  be  produced  by  the  simple 
pressure,  or  indeed  contact,  of  two  dissimilar  insulators. 
The  electricity  will  be  retained  by  the  insulators  after  their 
separation.  This  is  precisely  analogous  to  the  production 
of  electricity  by  the  contact  of  two  conductors. 

§  22.  Certain  minerals  when  warmed  acquire  an  electric 
charge,  differing  in  sign  at  different  parts  of  the  mineral ; 
thus,  one  end  of  a  heated  crystal  of  tourmaline  will  be 
positively  electrified,  while  the  other  is  negatively  electrified. 
This  electricity  is  sometimes  called  pyro-electricity.  The 
phenomenon  has  not  been  much  studied ;  the  electrical 
charge  is  probably  due  to  a  polarity  in  the  structure  of  the 
tourmaline  at  different  parts,  which  virtually  makes  in  one 
crystal  a  system  like  that  of  a  magnet  having  opposite  pro- 
perties at  opposite  ends.  The  electrical  phenomena  pro- 
duced by  the  contact  of  dissimilar  metals  are  produced 
even  when  the  dissimilarity  consists  merely  in  the  difference 
of  temper  in  one  and  the  same  piece  of  metal.  A  soft  and 
a  hard  piece  of  brass  wire  behave  as  dissimilar  metals, 
although  their  chemical  composition  may  be  identical.  If 
this  view  be  correct,  we  may  say  that,  wherever  electricity 
is  directly  produced,  it  requires  the  contact  of  two  dissimilar 
materials. 

§  23.  The  attractions  and  repulsions  produced  by  elec- 
tricity have  hitherto  been  spoken  of  as  absolute,  or  as  being 
produced  under  all  circumstances ;  but  if  an  uninsulated  metal 
plate  D  (Fig.  14)  be  interposed  between  an  electrified  body  A 
and  the  insulated  suspended  pith  ball  B  all  attraction  or  repul- 


CHAP.  I.J  Electric  Quantity.  25 

sion  will  cease,  just  as  if  the  metal  plate  were  opaque  to  the 
electric  influence.  If,  however,  thet  metal  plate  or  screen 
be  insulated  (as  in  Fig.  15)  it  will  increase  the  attraction  or 
repulsion  instead  of  destroying  them.  These  two  apparently 
different  effects  are  due  to  the  different  distributions  of  elec- 
tricity produced  in  the  two  cases. 

Let  A  be  electrified  positively,  and  the  plate  D  be  uninsu- 
lated, then  on  the  side  next  A  a  negative  charge  will  be 
induced,  diffused  over  a  considerable  surface  ;  the  effect 
of  this  diffused  negative  charge  is  very  nearly  to  neutralise 
all  attractions  or  repulsions  due  to  A,  on  the  farther  side  of 
the  screen.  The  metal  cap  of  the  electroscope  (Fig.  4)  is  in- 
tended to  screen  the  gold  leaves  from  inductive  effects,  and 
should  not  be  insulated.  The  whole  glass  case  should  be 
coated  with  an  open  wire  case  for  the  same  reason. 

When,  however,  the  metal  plate  D  is  insulated  the  farther 

FIG.  14.  FIG.  15. 


side  of  D  becomes  positively  electrified  as  A  was,  the  charge 
on  the  side  n  near  to  A  and  the  charge  on  A  nearly  neutralise 
one  another  as  before ;  but  the  positive  charge  on  the  far 
side  /  of  D  is  thus  left  free  to  attract  or  repel,  and  the  result 
is  the  same  as  if  the  body  A  had  been  advanced  in  the  direc- 
tion of  the  screen  by  an  amount  equal  to  the  thickness  of  the 
screen. 

We  can  now  understand  the  reason  why  a  Leydcn  jar  con- 


26  Electricity  and  Magnetism.          [CHAP.  n. 

taining  a  very  large  quantity  of  electricity  neither  attracts 
nor  repels  light  bodies  in  its  neighbourhood.  The  effect  of 
the  more  concentrated  inner  charge  and  more  diffused  outer 
charge  is  such  that  one  precisely  neutralises  the  other.  This 
statement  is  here  made  as  of  a  fact  ascertained  by  experi- 
ment. It  can  also  be  theoretically  demonstrated. 


CHAPTER  II. 

POTENTIAL. 

§  1.  The  word  Potential,  introduced  by  Green,  has  only 
lately  been  generally  adopted  by  electricians,  and  is  still 
often  misunderstood  ;  it  expresses  a  very  simple  idea,  and  one 
quite  distinct  from  the  meaning  of  any  other  term  relating 
to  electricity. 

As  .already  explained  in  Chapter  I.  §  7  difference  of 
potential  is  that  difference  of  electrical  condition  which  de- 
termines the  direction  of  the  transfer  of  electricity  from  one 
point  to  another ;  but  electricity  cannot  be  so  transferred 
without  doing  work  or  requiring  work  to  be  done,  hence 
the  following  definition.  Difference  of  potentials  is  a  differ- 
ence of  electrical  condition  in  virtue  of  which  work  is  done  by 
positive  electricity  in  moving  from  the  point  at  a  higher  potential 
to  that  at  a  lower  potential,  and  it  is  measured  by  the  amount 
of  work  done  by  the  unit  quantity  of  positive  electricity  when 
thus  transferred.  The  idea  of  potential  essentially  involves 
a  relative  condition  of  two  points,  so  that  no  one  point  or 
body  can  be  said  simply  to  have  an  absolute  potential  but 
for  the  sake  of  brevity. 

The  potential  ofa  body  or  point  is  used  to  denote  the  differ- 
ence between  the  potential  of  the  body  or  point  and '  i 'he potential 
of  the  earth. 

These  definitions  require  considerable  illustration  before 
they  can  be  fully  understood. 


CHAP.  II.]  Potential.  27 

Electrified  bodies  repel  and  attract  one  another,  and  by 
a  slight  extension  of  language  we  say  that  a  quantity  of 
positive  electricity  attracts  a  quantity  of  negative,  but  repels 
a  quantity  of  positive  electricity.  If,  therefore,  we  move  a 
quantity  of  positive  electricity  towards  another  similar 
quantity  we  meet  with  a  resistance  capable  of  measure- 
ment, equal,  for  example,  to  the  weight  of  so  many  grains.  In 
overcoming  this  resistance  work  must  be  done,  precisely  as 
work  must  be  done  to  lift  a  pound  or  a  grain.  The  work 
done  in  moving  a  body  from  A  to  B  is  measured  by  the 
product  of  the  distance  multiplied  into  the  force  overcome ; 
if  the  weight  of  a  grain  be  the  unit  of  force  and  the  foot  the 
unit  of  distance,  the  unit  of  work  will  be  the  foot  grain.  If, 
then,  in  moving  a  certain  quantity  of  electricity  from  A  to  B 
we  overcome  a  resistance  of  ten  grains  through  a  space  of 
five  feet  we  do  work  equal  to  fifty  foot  grains  during  the 
operation.  On  the  other  hand,  the  repulsion  or  attraction 
of  electrified  bodies  tends  to  perform  work;  for  the  body  just 
brought  to  B  may  be  driven  back  to  A  by  the  force  of 
electricity  alone.  In  the  one  case,  work  is  said  to  be 
done  upon  the  electrified  body  in  consequence  of  its  electri- 
fication; in  the  other  case  it  is  done  by  the  electrified  body 
in  virtue  of  its  electrification  ;  less  accurately  we  might 
say  the  work  was  done  by  the  electricity,  or  performed  upon 
the  electricity ;  the  measure  of  the  work  is  the  same  in  the 
two  cases,  which  are  analogous  to  letting  a  body  fall  from 
the  level  A  to  the  level  B,  and  raising  it  up  again  from  B  - 
to  A. 

§  2.  An  electrified  body  moving  from  one  point  to  another 
may  at  one  time  require  work  done  upon  it  in  order  to 
overcome  the  resistance ;  at  another  part  of  the  journey  it 
may  pull  in  the  direction  it  is  going  and  then  work  is  done 
by  it  I  speak  here  only  of  the  work  done  or  required  in 
consequence  of  the  electrical  condition  of  the  body. 

The  whole  work  which  has  been  required  in  consequence 
of  electrical  attractions  or  repulsions  to  move  it  from  any 


28  Electricity  and  Magnetism.          [CHAP.  n. 

point  A  to  any  point  B  will  be  the  algebraic  sum  of  the  work 
done  by  and  done  upon  the  electrified  body,  the  first  being 
called  positive  and  the  second  negative  work. 

Thus,  if  in  moving  the  electrified  body  from  A  to  B,  we  first 
have  to  overcome  a  resistance,  and  do  work  upon  it  equal  to 
10  foot  grains,  whereas  afterwards  it  pulls  towards  B,  doing 
work  equal  to  30  foot  grains,  then  in  the  whole  passage 
from  the  point  A  to  the  point  B  the  work  done  by  the  body 
may  be  said  to  be  20  foot  grains;  it  is  true  that  during  one 
part  of  the  passage  it  did  more  than  this,  but  only  after 
having  required  aid  previously. 

The  path  followed  in  going  from  A  to  B  will  be  a  matter  of 
indifference  so  far  as  this  total  work  done  by  or  upon  the  body 
is  concerned.  We  have  a  precisely  analogous  case  in  gravi- 
tation: a  body  of  a  pound  weight  in  falling  from  a  height  of  40 
feet  to  a  height  of  20  feet  above  the  sea,  will  do  necessarily  20 
foot-pounds  of  work  in  virtue  of  that  fall,  no  matter  what  path 
it  follows.  We  may  lift  it  above  A  and  do  work  upon  it  by  lifting 
it  before  letting  it  fall,  still  the  whole  work  done  by  the  body 
in  its  passage  from  A  to  B  and  in  virtue  of  that  fall  will  be  20 
foot-pounds ;  it  may  fall  by  the  most  roundabout  or  the  most 
direct  road,  the  work  done  will  be  the  same ;  it  may  fall 
below  the  level  of  A,  and  bound  up  to  A  :  the  whole  sum 
of  the  work  will  be  unchanged,  depending  merely  on  the 
difference  of  level  between  the  first  and  second  spot.  This 
work  may  indeed  be  represented  in  various  ways :  thus,  if  the 
body  fall  direct  through  a  vacuum  the  work  appears  in  the 
form  of  what  is  called  actual  or  kinetic  energy ;  that  is  to  say, 
it  is  wholly  represented  by  the  motion  of  the  mass.  If,  on 
the  other  hand,  the  body  falls  slowly,  lifting  another  weight, 
the  work  will  be  represented  partly  by  the  weight  lifted, 
partly  by  the  heat  due  to  the  friction  of  the  mechanism ;  but 
the  work  done  by  a  body  due  to  its  fall  from  one  level  to 
another  is  constant  in  amount  however  various  in  form. 
The  work  done  in  overcoming  electrical  force  or  done  by 
electrical  force  is  subject  to  the  same  law 


CHAP.  II.]  Potential.  29 

§  3.  In  moving  a  weight  from  a  point  A  to  a  point  B  on 
the  same  level  no  work  on  the  whole  is  either  done  upon  or 
by  the  body  in  respect  of  its  weight ;  and  similarly  in  moving 
a  small  electrified  body  from  a  point  A  to  some  other  point  B, 
it  may  happen  that  the  point  B  is  so  situated  that  on  the 
whole  no  work  is  either  done  upon  or  by  the  body  in  re- 
spect of  the  electrical  forces  in  action  on  the  body.  In  that 
case  the  two  points  might  be  at  the  same  electrical  level 
or  height,  but  the  recognised  term  in  respect  of  electrical 
forces  is  potential ;  the  points  A  and  B  are  at  the  same 
potential.  If  our  small  electrified  body,  for  instance,  be 
moved  round  another  large  electrified  body,  neither  ap- 
proaching nearer  nor  receding  farther  from  it,  and  so  far 
from  all  other  conductors  as  not  to  be  sensibly  attracted  or 
repelled  by  them,  it  will  pass  along  a  path  every  point  of 
which  is  at  the  same  electric  potential. 

In  moving  any  actual  body  from  spot  to  spot  some  work 
must  always  be  performed  to  overcome  friction,  but  as  in 
moving  a  heavy  body  from  one  point  to  another,  at  the  same 
gravitation  potential  or  level,  no  work  is  required  in  respect 
of  its  gravitating  properties,  so  in  moving  an  electrified  body 
from  one  point  to  another  at  the  same  electrical  potential  no 
work  is  required  in  respect  of  its  electrical  properties, 
although  of  course  work  will  certainly  be  required  to  over- 
come friction  and  may  be  required  in  respect  of  gravitation 
if  the  body  be  raised  or  in  respect  of  inertia  if  we  accelerate 
the  motion  of  the  mass. 

§  4,  The  potential  of  a  body  is  the  excess  or  defect  of  its 
potential  above  or  below  that  of  the  earth  in  the  neighbour- 
hood— the  potential  of  the  earth  at  that  point  being  arbitrarily 
assumed  as  nil. 

The  potential  increases  in  proportion  to  the  increase  of 
work  done  by  any  given  quantity  of  electricity  in  moving 
from  the  point  to  the  earth ;  and  since  the  potential  is  pro- 
portional to  the  work  and  to  the  quantity  of  electricity 
transferred,  and  to  no  other  quantity,  the  potential  of  a  point 


3O  Electricity  and  Magnetism.         [CHAP.  n. 

is  measured  by  the  work  which  a  positive  unit  of  electricity 
does  in  passing  from  that  point  to  the  earth.  The  unit 
quantity  of  electricity  might,  so  far  as  this  definition  is 
concerned,  be  chosen  arbitrarily,  but  there  is  a  certain 
convenience  for  many  calculations  in  choosing  the  unit  as 
defined  in  Chapter  I.  §  17.  Every  point  everywhere  may  be 
said  to  be  at  a  certain  electric  potential,  just  as  every  point 
everywhere  may  be  said  to  be  at  a  certain  level  above  or 
below  a  datum  line  arbitrarily  chosen,  such  as  the  Trinity 
high-water  mark.  In  speaking  of  the  potential  at  a  point 
it  is  as  unnecessary  to  conceive  of  the  presence  of  any 
electricity  at  that  point  as  it  is  to  think  of  the  presence  of  a 
heavy  body  at  a  point  when  we  speak  of  its  height  above 
the  sea. 

§  5.  The  electric  potential  at  the  point  depends  on  the 
electrical  condition  of  all  bodies  in  the  neighbourhood ;  that 
is  to  say,  sufficiently  near  to  exercise  any  sensible  force  on 
a  small  electrified  body  at  the  point.  Moreover,  in  testing 
the  equality  of  the  potential  at  two  points  by  the  work 
done  upon  or  by  an  electrified  body  in  its  motion  from  one 
point  to  the  other  we  must  remember  to  choose  a  body  con- 
taining only  a  very  small  charge  of  electricity,  which  we 
will  call  the  test  charge ;  otherwise,  the  mere  presence  of 
this  test  body  or  test  charge  of  electricity  would  sensibly 
change  the  potential  at  the  point  at  which  it  was  at  the 
time  of  the  experiment;  increasing  or  decreasing  for  the 
time  being  the  work  which  must  be  done  in  order  to 
bring  any  other  small  quantity  of  electricity  to  that  point. 
At  first  it  might  appear  as  if  the  analogy  of  gravitaticn 
deserted  us  here,  but  that  is  not  so;  for  if  I  say  that 
two  points  A  and  B  shall,  relatively  to  the  earth,  be  at 
the  same  level  when  no  work  is  done  upon  or  by  a 
heavy  body  in  passing  from  one  to  the  other,  I  must 
remember  that  in  placing  a  heavy  body  at  the  point  A,  I  do 
change  for  the  time  the  gravitation  level  of  that  point  if  the 
body  be  of  sensible  size  compared  with  the  earth;  for  its 


CHAP.  II.]  Potential.  31 

presence  at  A  has  increased  the  attraction  of  all  other  heavy 
bodies  to  A,  so  that  for  the  time  being  a  small  weight 
passing  from  A  to  B  would  do  work;  the  position  of  the 
centre  of  gravity  of  the  earth  having  been  changed. 

§  6.  The  difference  of  potential  between  two  points  A  and  B, 
being  the  difference  of  condition  in  virtue  of  which  elec- 
tricity does  work  in  moving  from  one  to  the  other,  is  measured 
by  the  work  required  to  move  a  unit  of  electricity  against 
electric  repulsion  from  A  to  B,  or,  what  is  the  same  thing, 
it  is  measured  by  the  work  which  a  unit  of  electricity  would 
do  while  being  impelled  from  B  to  A. 

The  point  A  is  said  to  have  a  higher  potential  than 
B  if  a  unit  of  positive  electricity  in  passing  from  A  to  B 
performs  work.  It  is  assumed  that  the  unit  of  electricity 
does  not  disturb  the  distribution  of  electricity  in  the  neigh- 
bourhood. 

The  conception  of  the  work  which  must  be  done  upon  or 
by  electricity  in  passing  from  one  point  to  another  must 
be  grasped  as  the  only  idea  which  can  explain  difference 
of  potential.  When  bodies  are  spoken  of  as  being  in  the 
same  electrical  condition  we  mean  that  they  are  at  the  same 
potential.  Difference  of  potential  can  therefore  be  expressed 
in  foot  grains  or  any  other  recognised  unit  of  work. 

In  this  paragraph  the  work  is  spoken  of  as  being  done  by 
the  unit  of  electricity  simply  to  avoid  the  awkward  periphrasis 
*  done  by  a  small  electrified  body  charged  with  one  unit  of 
electricity '  and  '  done  in  consequence  of  the  electric  charge 
only.'  That  is  to  say,  it  is  the  extra  work  which  must  be 
done  in  moving  the  body  from  the  one  place  to  the  other  in 
consequence  of  its  being  electrified. 

§  7.  Let  us  apply  our  definition  to  special  cases.  First, 
take  an  electrified  conductor  on  which  electricity  is  at  rest, 
having  assumed  that  distribution  which  is  determined  by 
its  own  shape  and  the  shape  and  position  of  neighbouring 
conductors.  All  points  on  the  surface  of  such  a  conductor 
are  at  the  same  potential.  If  any  one  point  A  were  at  a 


32  Electricity  and  Magnetism.  [CHAP.  II. 

higher  potential  than  another  B,  the  electricity  at  A  would 
as  surely  run  to  B  as  a  weight  would  fall  from  a  higher  level 
to  a  lower  unless  resisted  by  some  force ;  whereas,  on  the 
conductor  there  is  no  impediment  to  the  free  motion  of 
electricity.  One  end  of  the  conductor  may  be  positively 
electrified,  the  other  end  negatively  electrified  ;  the  centre 
may  have  no  sensible  charge  as  in  the  body  B,  Fig.  6  ;  never- 
theless all  points  of  the  surface  are  at  the  same  potential,  for 
I  might  move  any  little  electrified  body  all  over  the  surface 
without  its  being  retarded  or  impelled  in  any  direction  by 
electrical  forces.  All  points  in  the  interior  of  the  conductor 
are  also  at  the  same  potential  as  the  surface,  although  no 
charge  of  electricity  is  ever  found  at  any  internal  point. 

The  little  test  charge  of  electricity,  when  introduced  into 
any  cavity  in  the  interior  of  a  body,  would  be  equally  ready 
to  move  in  all  directions,  and  would  be  in  perfect  equili- 
brium. At  first  it  might  seem  that  inside  or  outside  the 

body  a  unit  of  positive  elec- 
tricity a  (Fig.  1 6)  would  be 
attracted  by  that  end  N  of  the 
conductor  N  p  which  was  ne- 
gatively charged,  and  would 
be  repelled  by  the  other  end  p ; 

but  in  thinking  thus  we  forget  the  influence  of  the  external 
neighbouring  conductor  M,  which  has  already  produced 
the  arrangement  of  the  charge  upon  N  P.  The  test  charge, 
wherever  applied,  will  not  tend  to  move  in  one  direction 
more  than  another,  but  to  subdivide  itself  over  the  large 
conductor  N  p,  in  the  same  manner  as  the  original  charge 
is  distributed. 

§  8.  Let  us  next  consider  the  space  round  a  charged  con- 
ductor, this  space  being  necessarily  filled  with  air  or  some 
other  insulator.  First,  conceive  the  conductor  to  be  uni- 
formly charged  with  one  kind  of  electricity,  as  a  sphere  might 
be  in  the  centre  of  a  spherical  room  (Fig.  17).  Then  the 
space  close  to  the  sphere  would  be  very  nearly  at  the  same 


CHAP.  II.]  Potential.  35 

potential  as  the  sphere,  for  our  test  charge  of  electricity 
would  do  very  little  work  in  moving  up  to  the  sphere  if 
attracted  to  it,  and  would  require  little  work  to  be  done 
upon  it  to  move  it  up  to  the  sphere  against  the  repelling 
force.  Let  us  conceive  the  potential  of  the  sphere  to  be 
positive  and  the  test  charge  positive  also.  Then  the 
potential  of  the  space  round  the  sphere  falls,  or  becomes 
less  positive  as  we  recede  from  the  sphere.  The  work 
required  to  bring  the  test  charge  to  the 
ball  increases  as  it  is  removed  farther 
and  farther  from  the  ball,  although  the 
force  with  which  it  is  repelled  dimi- 
nishes. Again,  the  case  is  analogous 
to  that  of  gravitation.  The  work  which 
a  body  will  do  falling  to  the  earth  in- 
creases as  the  height  increases  from 
which  it  falls,  although  the  attraction 
between  the  earth  and  the  body  diminishes  as  it  recedes 
from  the  earth. 

§  9.  As  the  test  charge  approaches  the  wall  of  the  room 
surrounding  our  positively  charged  sphere,  it  approaches  a 
negative  charge  of  electricity,  and  is  more  and  more  attracted 
by  it;  this  attraction  further  increases  the  work  required  to 
bring  the  test  charge  back  to  the  electrified  sphere,  and  the 
potential  falls  faster  and  faster.  The  fall  continues  until  the 
test  charge  touches  the  wall  of  the  room,  which  is  thus  shown 
to  be  necessarily  at  a  lower  potential  than  the  charged 
sphere.  Had  we  begun  with  a  negative  charge  on  the 
internal  sphere,  we  should  have  found  that  the  wall  of  the 
room  would  have  been  at  a  higher  potential  than  the  sphere. 
Thus  we  find  that  there  is  a  necessary  difference  of  potential 
between  the  inner  and  outer  coating  of  a  Leyden  jar,  or 
generally  that  any  two  conductors  between  which  induction 
is  taking  place  must  be  at  different  potentials. 

The  potential  diminishes  gradually  from  the  internal  sphere 
to  the  surrounding  conductor,  and  all  concentric  spherical 


34  Electricity  and  Magnetism.         [CHAP.  u. 

surfaces  will  be  at  one  potential,  i.e.  we  might,  so  far  as 
electrical  forces  are  concerned,  without  doing  or  receiving 
any  work,  move  the  test  charge  all  over  any  concentric 
spherical  surface,  indicated  by  the  lines /i,/2,/3,  in  Fig.  17. 
Whatever  be  the  shape  of  the  internal  electrified  body,  I 
may  conceive  in  the  dielectric  surrounding  it  equipotential 
surfaces  of  this  kind,  the  form  of  which  will  depend  on  the 
form  of  the  internal  and  external  conductors. 

We  may  further  conceive  successive  equipotential  surfaces 
separated  by  such  distances  that  the  same  amount  of  work 
would  be  done  by  the  test  charge  in  moving  from  any  one  to 
the  next.  An  equal  amount  of  work  would  be  required  to 
move  the  test  charge  back  from  any  one  of  these  surfaces  to 
that  adjacent  to  it  and  at  a  higher  potential. 

§  10.  Consider  the  more  complex  case  of  a  body  charged 

partly  with  positive  and  partly  with  negative  electricity  but 

all  at  one   potential.     This   in- 

FIG.  18.  ,  ..  ...... 

volves  a  complicated  distribution 
of  electricity  in  neighbouring 
conductors,  such,  for  instance, 
as  is  shown  in  the  annexed  dia- 
gram (Fig.  1 8). 

Very  near  the  surface  of  the 
conductor  A,  the  potential  of  the 
dielectric  will  be  sensibly  the  same  as  that  of  A,  and  there 
is  nothing  here  to  indicate  whether  the  potential  of  A  is 
positive  or  negative  relatively  to  the  general  enveloping 
conductor  B;  but  receding  from  A  towards  c  the  potential 
of  the  space  falls,  whereas,  as  we  pass  from  A  towards  D,  it 
rises ;  again,  receding  from  D  towards  the  envelope  B,  the 
potential  falls,  but  as  we  pass  from  c  to  the  envelope  the 
potential  rises,  so  that  close  to  B  the  potential  is  the  same 
at  all  points,  but  whether  higher  or  lower  as  a  whole,  there 
is  nothing  in  the  diagram  to  tell  us.  All  these  conclusions 
are  deduced  from  the  simple  conception  of  the  work  required 
to  move  our  imaginary  test  charge  from  place  to  place.  Nor 


CHAP.  II.]  Potential.  35 

can  any  simpler  conception  be  suggested.  We  see  from  the 
above  diagram,  that  a  body  charged  with  negative  electricity 
might  have  a  positive  potential  relatively  to  a  point  charged 
with  positive  electricity,  and  vice  versd.  For  the  body  A 
may  all  be  at  a  positive  potential  relatively  to  the  body  B, 
notwithstanding  the  fact  that  the  part  a  of  this  conductor 
is  negatively  charged  while  some  point  of  B,  such  as  £,  is 
positively  charged. 

§11.  The  charge  induced  between  two  opposed  con- 
ductors separated  by  a  dielectric,  implies  a  difference  of 
potential  between  the  conductors  as  shown  above.  More- 
over, as  the  difference  of  potentials  increases,  so  must  the 
induced  charges  increase,  for  in  order  to  make  it  more  and 
more  difficult  to  move  the  test  charge  from  one  surface  to 
the  other,  the  repulsion  from  one  side  and  attraction  to  the 
other  must  increase,  and  this  additional  attraction  and 
repulsion  can  only  be  increased  by  increasing  the  quantities 
of  electricity.  On  the  other  hand,  so  long  as  the  difference 
of  potentials  between  the  surfaces  remains  constant  the 
charge  on  the  opposing  surfaces  must  remain  constant;  both 
potentials  may  rise  and  fall  together,  but  the  constant 
difference  of  potential  implies  a  constant  internal  charge. 
An  example  will  make  the  meaning  of  this  statement  clear. 
Suppose  an  ordinary  Leyden  jar  to  be  charged  with  negative 
electricity  and  to  have  its  outer  coating  in  connection  with 
earth.  The  potential  of  the  inner  coating  will  be  negative, 
relatively  to  the  earth ;  and  calling  the  potential  of  the  earth 
zero,  as  is  usually  done  for  brevity,  we  may,  as  stated  in 
§  4,  simply  say  that  the  potential  of  the  inner  coating  of  our 
jar  is  negative.  There  will  be  a  positive  charge  of  electri- 
city on  the  inside  of  the  outer  coating  of  the  jar  equal  to  the 
negative  charge  within. 

Insulate  the  outer  coating,  and  electrify  it  with  a  positive 
charge.  Its  potential  will  be  raised,  but  the  potential  of  the 
inner  coating  will  be  raised  by  a  like  amount.  The  negative 
charge  will  remain  inside  the  jar  undisturbed  in  amount; 

1)  2 


36  Electricity  and  Magnetism.         [CHAP.  n. 

opposite  to  it  will  remain  the  positive  charge  on  the  inner 
side  of  the  outer  coating,  the  only  change  being  that  on  the 
outer  side  of  the  outer  coating  we  have  now  a  positive 
charge.  The  effect  of  this  additional  positive  charge  will  be 
to  increase  the  work  required  to  bring  our  test  charge  from 
a  distance  up  to  the  jar,  or  to  any  point  inside  the  jar,  Le. 
the  potential  both  of  inside  and  outside  and  of  all  adjacent 
points  has  been  raised. 

§  12.  Next,  suppose  that  two  jars  (Fig.  19),  having  their  inner 
coatings  in  electrical  connection,  are 
F|G>  T»  charged  with  negative  electricity,  the 

outer  coatings  being  uninsulated,  i.e. 
at  the  potential  of  the  earth.  The 
potential  of  the  inner  coatings  will 
be  negative,  and  if  the  two  jars  are 
equal  in  all  respects,  the  negative 
charge  in  each  will  be  equal  In- 
sulate jar  A,  and  increase  the  poten- 
tial of  its  outer  coating  by  electrirying  it  positively.  The 
negative  charge  will  now  redistribute  itself  between  the 
jars. 

The  potential  of  the  outer  coating  of  B  remains  constant 
The  potential  of  the  inner  coatings  of  A  and  B  must  be 
uniform  throughout,  since  they  are  in  metallic  connection. 
Their  potential  as  a  whole  win  be  somewhat  raised,  but 
not  so  much  as  that  of  the  outer  coating  of  A  ;  hence  the 
difference  of  potentials  between  the  coatings  of  A,  will  have 
been  increased,  and  its  internal  charge  will  have  increased, 
and  this  will  have  occurred  at  the  expense  of  B,  where  the 
difference  of  potentials  between  the  inner  and  outer  coatings 
will  have  diminished. 

§  13.  If  one  coating  of  any  Leyden  jar  be  kept  at  a 
constant  potential,  such  as  that  of  the  earth  at  the  spot  is 
generally  assumed  to  be,  the  quantity  of  electricity  which 
the  other  coating  contains  is  simply  proportional  to  its  poten- 
tial, a/act  determined  by  experiment  Thus,  if  I  have  the 


CHAP.  II.] 


Potential. 


37 


means  of  producing  a  constant  potential,  or  rather  a  constant 
difference  of  potential,  from  that  of  the  earth,  I  shall  also 
have  the  means  of  collecting  a  constant  quantity  of  electri- 
city. The  charge  assumed  by  any  insulated  conductor  inside 
a  conducting  envelope,  however  far  remote,  is  simply  propor- 
tional to  the  difference  of  potentials  between  the  envelope 
and  insulated  conductor ;  and  as  a  limit  we  may  say  that 
the  charge  on  any  insulated  conductor,  when  there  are  no 
electrified  bodies  in  the  neighbourhood,  is  simply  propor- 
tional to  the  potential  of  the  conductor  ;  that  is  to  say, 
the  difference  of  its  potential  from  that  of  the  earth.  The 
force  it  exerts  is  proportional  to  the  quantity,  and  the  work 
required  to  overcome  that  force  is  proportional  to  the 
force. 

§  14.  In  a  Leyden  jar  it  is  immaterial  which  of  the 
coatings  is  in  connection  with  the 
earth,  or  whether  either  of  them  be 
so.  Connection  with  the  earth  is 
merely  a  device  for  keeping  the  po- 
tential of  that  particular  coating  con- 
stant, or  nearly  so,  by  maintaining  it 
in  connection  with  a  very  large  con- 
ductor. Thus,  the  inner  coating  of  a 
jar  when  in  connection  with  the  earth, 
will  take  a  negative  charge  if  the  outer 
coating  be  positively  electrified,  and, 
the  difference  of  potentials  being  the 
same,  this  charge  will  be  precisely  the 
same  in  amount  as  if  the  outer  coating  had  been  in  con- 
nection with  the  earth,  and  the  inner  coating  had  been 
directly  electrified  by  negative  electricity. 

§  15.  Let  us  consider  the  construction  of  electroscopes 
by  the  light  of  the  knowledge  we  have  now  acquired;  for 
instance,  the  gold  leaf  electroscope,  Fig.  20. 

The  repulsion  between  the  two  gold  leaves  a  and  b  de- 
pends on  the  quantity  of  electricity  with  which  they  are 


38  Electricity  and  Magnetism.         [CHAP.  II. 

charged.  But  upon  what  does  this  quantity  itself  depend  ? 
Merely  on  the  difference  of  potential  between  the  gold  leaf 
and  the  conductors  c  and  d  immediately  surrounding  it. 
When  the  gold  leaves  a  and  b  are  connected  with  the 
electrified  body  A  to  be  examined,  a  b  and  A  assume 
the  same  potential;  then  the  quantity  of  electricity  ac- 
cumulated on  the  gold  leaf  depends  on  the  difference 
of  that  potential  from  the  neighbouring  conductors  c 
and  d\  let  c  and  d  be  insulated,  and  at  the  same  poten- 
tial as  A,  then,  no  matter  how  much  electricity  there 
may  be  on  A,  none  will  come  to  a  and  £,  and  no  diver- 
gence will  occur  in  the  leaves.  In  the  ordinary  construc- 
tion of  electroscopes,  some  parts  of  the  surrounding  con- 
ductors c  and  d  are  glass,  and  their  potential  depends  on 
conditions  over  which  we  have  no  control ;  c  and  d  should 
be  in  a  metal  case  with  openings,  to  allow  a  and  b  to  be  seen ; 
for  instance,  a  wire  cage  round  glass,  the  meshes  of  which 
approach  sufficiently  near  to  keep  the  whole  surface  of  the 
glass  at  one  potential ;  then,  if  c  and  d  be  in  connection  with 
the  earth,  a  and  b  will  be  charged  with  electricity  whenever 
there  is  a  difference  of  potential  between 
FIG.  21.  A  and  the  earth.  Exactly  similar  reason- 

ing applies  to  the  Peltier  electroscope, 
Fig.  21.  In  this  instrument  instead  of 
the  gold  leaf  we  have  a  rod  a  b,  free  to 
move  on  a  vertical  axis  v,  and  repelled  at 
each  end  by  a  fixed  conductor  c  d  in 
electrical  connection  with  it,  but  placed 
on  an  insulating  support  D;  the  rod  is 
directed  by  a  small  magnet  m  n ;  the  in- 
strument is  so  placed  that  when  c  d  has 
f  no  charge  of  electricity,  the  magnet  places 
the  rod  just  clear  of  these  fixed  conductors 
c  and  d ;  then  when  B  with  a  b  are  all  charged  with  electricity, 
the  rod  a  b  is  repelled  until  the  force  of  electric  repulsion  is 
just  balanced  by  the  directing  force  of  the  magnet.  The 


CHAP.  II.]  Potential.  39 

force  depends  on  the  quantity  of  electricity  on  the  rod  and 
balls,  but  this  quantity  is  proportional  to  the  difference  of 
potential  between  the  system  B  c  d,  &c.,  and  the  enveloping 
conductor  A,  which  is  not  shown  in  the  drawing  but  which 
encloses  the  whole  insulated  system  B  c  d.  This  electroscope, 
therefore,  like  the  preceding  one,  and  like  all  others,»indi- 
cates  difference  of  potential  by  means  of  the  quantity 
which  that  difference  causes  to  accumulate  on  an  insulated 
conductor. 

In  the  instruments  usually  made  there  is  a  divided  ring  to 
show  how  far  the  rod  a  b  is  deflected.  The  instrument 
indicates  more  conveniently  than  the  gold  leaf  electroscope 
whether  a  given  potential  be  higher  or  lower  than  another ; 
but  inasmuch  as  the  deflections  are  not  proportional  to  the 
difference  of  potential  between  a  b  and  the  case  A,  and  are 
not  even  connected  by  any  simple  law  with  this  difference 
of  potential,  the  Peltier  electroscope  cannot  be  used  to 
measure  difference  of  potentials,  i.e.  to  compare  two  poten- 
tials or  differences  of  potentials  accurately,  so  as  to  allow  us 
to  say  that  one  is  distinctly  two,  three,  or  four  times  as  great 
as  another.  For  this  purpose  we  require  much  more  com- 
plex arrangements,  electrometers  or  instruments  in  which 
the  attractions  and  repulsions  produced  by  given  differences 
of  potential  between  the  parts  can  be  calculated  definitely. 

All  electrometers  measure  directly  differences  of  potentials, 
and  measure  quantities  only  indirectly. 

§  16.  If  two  electrified  conductors  A  and  B,  which  are 
at  the  same  potential,  be  joined  by  a  wire,  no  disturbance 
in  the  electric  distribution  on  the  system  will  take  place, 
unless  indeed  the  wire  be  of  sensible  size  relatively  to  the 
other  conductors,  and  at  a  different  potential ;  but,  assum- 
ing the  wire  to  be  small,  or  at  the  same  potential  as  A  and 
B,  the  electricity  on  the  bodies  after  being  joined  will  be  in 
equilibrium  as  before,  the  necessary  condition  of  equality 
of  potential  throughout  being  satisfied.  If,  on  the  other 
hand,  A  be  at  a  higher  potential  than  B,  positive  electricity 


4O  Electricity  and  Magnetism.          [CHAP,  n, 

must,  when  the  connection  is  made,  flow  from  A  to  B,  to 
re-establish  electric  equilibrium.  The  amount  of  the  elec- 
tricity thus  transferred  must  be  such  as  will  restore  the 
equilibrium ;  it  will  be  great  when  the  difference  of  poten- 
tial is  great  and  when  the  size  of  the  bodies  is  large,  and 
small  under  the  opposite  conditions.  The  existence  or 
continuance  of  the  flow  of  electricity  from  one  point  to 
another  depends  solely  on  the  difference  of  potential 
between  the  points.  The  magnitude  of  the  conductors  has 
only  one  influence  in  the  result,  by  requiring  that  a  larger 
quantity  of  electricity  shall  flow  to  re-establish  equilibrium. 
We  may  illustrate  this  by  an  experiment  with  water.  If  we 
join  two  reservoirs  of  water,  big  or  little,  by  a  pipe,  no 
now  takes  place  from  one  to  the  other  if  the  surfaces  of 
the  water  in  both  are  at  the  same  level.  If  they  be  not, 
the  flow  will  take  place  from  the  higher  to  the  lower ;  the 
quantity  of  fluid  transferred  depends  on  the  capacity  of  the 
reservoirs  and  original  difference  of  level:  it  continues 
until  the  level  is  the  same  in  both.  Substitute  potential  for 
level,  electricity  for  water,  conductor  for  reservoir,  and  the 
above  statements  are  all  true  for  electricity. 

§  17.  If  I  put  one  end  of  a  wire  in  connection  with  the 
earth  and  the  other  at  a  point  x  in  the  air  (which  may 
be  at  a  very  high  potential)  no  electricity  flows  through 
my  wire  from  the  point  to  the  earth,  simply  because  at 
the  point  in  question  there  was  no  electricity  to  flow,  its 
capacity  and  charge  being  zero  ;  but  the  potential  of  the 
point  will  have  been  changed  by  the  mere  presence  of  the 
wire  to  that  of  the  earth.  For  this  purpose,  while  the 
wire  was  approaching  the  point,  a  redistribution  of  electri- 
city on  its  surface  has  been  going  on  under  the  influence  of 
the  induction  to  which  the  potential  of  point  x  was  due. 

If  the  wire  has  a  sharp  point  so  that  a  very  small  quantity 
of  electricity  will  produce  a  great  density,  electricity  will 
actually  flow  from  the  air  to  the  earth;  successive  particles  of 
air  negatively  charged  will  fly  from  the  point,  and  be  replaced 


CHAP.  II. i  Potential.  41 

by  particles  of  air  positively  charged,  each  of  which  will  be 
discharged  through  the  wire.  If  the  potential  of  the  point 
be  sufficiently  high  the  phenomenon  is  accompanied  by  noise 
and  a  brush  of  light.  A  lighted  match  on  the  end  of  the 
wire  also  allows  the  transfer  of  electricity  to  take  place;  the 
burnt  particles  fly  off  with  the  charge  of  one  sign  and  the  air 
about  to  be  burnt  brings  electricity  of  the  other  sign  to  the 
wire. 

§  18.  By  definition  the  difference  of  potential  was  de- 
clared to  depend  on  the  work  done  by  or  upon  electricity 
in  moving  from  one  point  to  another.  The  nature  of  the 
work  done  by  or  to  a  quantity  of  electricity  moved  on  a 
conductor  by  or  against  a  force  of  attraction  or  repulsion  is 
clear  enough — a  tangible  force  is  used  or  overcome  ;  a  solid 
body  is  either  put  in  motion,  or  its  motion  is  resisted;  but 
when  electricity  moves  along  a  wire  from  a  body  at  one  po» 
tential  to  a  body  at  another,  no  solid  body  is  moved  at  all, 
and  no  equivalent  work  appears  at  first  sight  to  have  been 
done.  The  equivalent  is  found,  however,  in  heat  generated 
in  the  wire  by  the  passage  of  the  electricity.  It  is  well 
known  from  the  research  of  Joule  that  772  foot-pounds  of 
work  are  equivalent  to  the  quantity  of  heat  which  raises  i  Ib. 
of  water  i°  Fahr.,  and  although  no  visible  mechanical  work  is 
done,  where  a  quantity  Q  of  electricity  passes  along  a  wire  from 
A  to  B,  heat  is  generated  precisely  equivalent  in  amount  to 
the  work  which  the  attractions  and  repulsions  of  the  elec- 
trified bodies  A  and  B  would  have  done  when  acting  upon 
the  same  amount  of  electricity  Q,  conveyed  on  a  small 
moving  conductor  from  the  body  A  to  the  body  B.  We 
shall  find  that  electricity  in  motion  is  capable  of  doing 
work  in  other  ways,  but  in  whatever  way  work  or  its  equiva- 
lent is  produced  by  electricity  moving  from  A  to  B,  the  amount 
will  always  be  equal  to  the  quantity  of  electricity  transferred 
multiplied  into  the  excess  of  potential  of  A  over  B. 

§  19.  Difference  of  potential  may  be  produced  by  mere 
induction.  A  small  insulated  conductor  placed  at  any  point 


42  Electricity  and  Magnetism.          [CHAP.  IT. 

in  space  where,  owing  to  the  neighbourhood  of  electrified 
bodies,  the  potential  was  x,  will  itself  assume  the  potential  x, 
without  losing  or  gaining  any  electricity.  Then  if  this  body 
be  connected  with  the  earth,  electricity  will  flow  from  the 
body  to  or  from  the  earth  sufficient  in  amount  to  bring 
the  body  to  the  potential  of  the  earth  ;  if  x  be  positive,  the 
current  will  be  to  the  earth  ;  if  x  be  negative,  the  current 
will  be  from  the  earth  to  the  body. 

§  20.  Difference  of  potential  is  produced  by  friction 
between  insulators  followed  by  separation.  Two  insulators 
rubbed  against  each  other  become  oppositely  charged, 
and  there  is  a  difference  of  potential  between  them.  It 
is  probable  that  for  each  pair  of  substances  rubbed  to- 
gether there  is  a  certain  maximum  difference  of  potential 
which  cannot  be  exceeded.  The  list  already  given,  Chapter 
I.  §  9,  showing  the  order  in  which  some  materials  stand,  so 
that  each  becomes  positive  when  rubbed  by  any  of  the  sub- 
stances placed  after  it,  necessarily  shows  also  the  order  in 
which  materials  must  be  classed,  so  that  when  one  is  touched 
or  rubbed  by  another  following  it  in  the  list,  the  potential  of 
the  former  may  become  positive  relatively  to  that  of  the 
latter.  Moreover,  a  greater  difference  of  potential  is  pro- 
duced by  friction  between  substances  far  apart  on  the  list 
than  between  substances  close  together  on  the  list.  It  is 
possible  that  the  law  which  will  in  the  next  paragraph  be 
enunciated  for  conductors  may  also  hold  good  for  insu- 
lators. 

§  21.  When  two  dissimilar  conductors  touch  one  another, 
a  difference  of  potential  is  produced  between  the  conductors 
charging  them,  as  mentioned  Chapter  I.  §  19.  The  dif- 
ference of  potential  is  constant  with  constant  materials,  i.e. 
copper  and  zinc  at  a  given  temperature  touching  one  another 
are  invariably  at  potentials  differing  by  a  constant  measurable 
amount.  The  same  may  be  said  of  any  two  metals.  Moreover, 
all  metallic  conductors  may  be  ranged  in  a  list,  such  that  any 
one  of  them  in  contact  with  any  of  the  conductors  later  in  the 
list  will  have  a  potential  positive  relatively  to  that  conductor. 


CHAP.  II.]  Potential.  43 

Moreover,  calling  these  bodies  A  B  c  D,  &c.,  the  difference 
of  potential  between  A  and  c  is  equal  to  the  difference 
of  potential  between  A  and  B  added  to  the  difference  of 
potential  between  B  and  c,  or  generally  if  these  bodies  were 
all  in  contact  one  with  another  in  the  order  A  B  c  D  .  .  .  N, 
&c.,  and  if  we  call  a  b  c  d .  .  .  n,  &c.,  the  potentials  of 
these  bodies,  a  —  n  =  (a  —  b)  4-  (b  —  c]  +  (c  —  d} 
.  .  .  +  (m  -  n).  Thus  if  three 
bodies  be  in  contact,  as  in  Fig.  22, 

the  difference  of  potential  between      ^— — r^ T , 

,f                         ,                Gold    \Cofper    Zwc 
the  ends  A  and  E  may  be  calcu-      >• ' ' ^ 

lated  from  the  two  end   metals 

only  ;  in  the  example  given,  it  does  not  matter  what  the 
difference  of  potentials  between  gold  and  copper  alone 
would  be,  for  call  that  a,  and  call  the  difference  between 
gold  and  zinc  c,  and  that  between  copper  and  zinc  #,  then 
(a  —  b)  +  (b  —  c)  =  a  —  c,  as  if  gold  and  zinc  had  been 
directly  in  contact.  It  may  be  stated  quite  generally  that  in 
any  series  of  metallic  conductors  thus  placed  in  contact,  the 
difference  of  potentials  between  the  ends  depends  on  the 
extreme  conductors  of  the  series.  The  following  is  a  list  of 
conductors,  ranged  in  such  an  order  that  each  becomes 
positive  when  touched  by  those  which  follow.  Zinc,  -lead, 
tin,  iron,  antimony,  bismuth,  copper,  silver,  gold.  The 
earlier  metals  on  the  list  are  called  electropositive  to  those 
which  follow.  The  exact  relative  differences  of  potential 
have  as  yet  been  experimentally  ascertained  only  in  a  few 
cases. 

§  22.  It  is  believed  that  all  compound  solid  bodies  which 
are  conductors  behave  in  the  same  way  as  simple  metallic 
conductors  so  far  as  the  production  of  a  difference  of  poten- 
tial due  to  mere  contact  is  concerned,  and  this  is  certainly 
the  case  in  many  instances.  Liquid  conductors  also  appear 
relatively  to  one  another  to  form  a  series  of  the  same  kind. 
But  compound  liquids  and  solids  do  not  admit  of  being 
arranged  relatively  to  one  another  in  the  simple  order 
described  as  applicable  to  metals. 


44 


Electricity  and  Magnetism.          [CHAP.  II. 


This  difference  between  the  compound  liquid  and  the 
simple  metallic  conductor  appears  to  be  intimately  con- 
nected with  the  fact,  that  electricity  in  passing  through  these 
compounds  decomposes  them,  a  phenomenon  to  be  more 
especially  described  hereafter.  The  compounds  which  are 
thus  decomposed  are  called  electrolytes.  The  following 
series  of  phenomena  occur  when  metals  and  electrolytes  are 
placed  in  contact: — 

FIG.  23.  FIG.  23A. 

Cop.          Cop.     Zinc  Cop. 


Fckcntidl.  diay. 


1.  When  a  single  metal  is  placed  in  contact  with  a  liquid 
electrolyte,  a  definite  difference  of  potentials  is  produced 
between  the  liquid  and  the  metal.     For  the  same  metal  and 
liquid  the  difference  is  constant  at  the  same  temperature 
under  all  circumstances,  but  slight  differences  of  condition 
in  the  metal  and  liquid  often  cause  considerable  changes  in 
the  difference  of  potential  observed. 

2.  When  two  metals  not  in  contact  are  plunged  into  a 
liquid  electrolyte,  as  in  Fig.  23,  each  surface  of  separation 
produces  its  effect  independently  of  the  other,  so  that  the 
difference  of  potentials  between  the  metals  will  be  the  sum 
of  the  differences  between  each  metal  and  the  liquid,  these 
differences   being  reckoned   in   one   direction.      Thus   for 
copper,  zinc,  and  zinc  sulphate  solution,  let  the  following 
numbers  denote  in  a  certain  unit  (Volt.)  the  difference  of 
potentials  between  the  substances.     The  sign  indicates  that 
the  substance  first  named  is  positive  or  negative  relatively  to 
that  last  named. 


CHAP.  II.]  Potential.  45 

Copper  ....  zinc  sulphate  sol — 0*113 

Zinc  sulphate  sol zinc +0*358 

When  as  in  Fig.  23  the  two  metals  are  simply  immersed  in 
the  solution  we  have  for  the  series  copper  .  .  .  zinc  sulph. 
sol.  .  .  .  zinc,  a  difference  of  potentials— cr  113  +  0-358 
=  +  -245  the  copper  will  be  positive  relatively  to  the  zinc  to 
the  extent  of  0-245  um>t- 

3.  Next  let  a  piece  of  the  same  copper  plate  be  joined 
to  the  zinc  so  as  to  form  the  complete  galvanic  cell  shown 
in  Fig.  23A,  and  let  the  difference  of  potential  due  to  the 
contact  zinc  .  .  .  copper  be  +075  ;  then  as  before  each 
surface  of  separation  produces  its  whole  difference  of 
potentials,  and  the  difference  between  the  first  and  last 
substance  of  the  series  win1  be  the  algebraic  sum  of  the 
separate  differences  each  reckoned  in  the  same  direction. 
This  total  difference  will  therefore  be  —0-113  +  0 -3 58  +  075 
=  +  0-995,  tne  copper  plunged  in  the  solution  will  be 
positive  relatively  to  the  copper  attached  to  the  zinc,  and 
the  difference  between  them  will  be  nearly  one  unit. 

If  a  series  of  galvanic  cells  be  joined  (as  in  Fig,  13)  the 
difference  between  the  first  copper  plate  and  the  copper 
wire  attached  to  the  last  zinc  will  be  equal  to  the  sum  of  the 
differences  produced  at  all  the  surfaces  of  separation,  or  in 
other  words  to  the  sum  of  the  differences  produced  by  each 
cell.  Thus,  40  cells  will  give  a  difference  of  potentials 
40  x  0-995  or  39*8  in  the  unit  chosen. 

The  distribution  of  potential  in  the  cell  complete  and  in- 
complete is  shown  in  the  diagrams  beneath  Figs.  23  and  23A. 

In  some  cases  the  differences  of  potentials  between  two 
metals  and  one  electrolyte  (Fig.  23)  may  when  added  cancel 
one  another.  The  two  metals  will  then  be  at  one  potential. 
Volta  believed  this  was  always  the  case,  and  this  theory  was 
provisionally  adopted  in  the  earlier  editions  of  this  work  in 
consequence  of  an  experiment  by  Sir  William  Thomson,  to 
be  presently  described,  in  which  the  cancelling  actually  does 
take  place.  The  theory  now  given  is  based  on  experiments 
by  Gerland,  Messrs.  Perry  and  Ayrton,  and  Professor 


46  Electricity  and  Magnetism.          [CHAP.  II. 

Clifton.     Further  developments  of  the  theory  will  be  found 
in  Chap.  XV.  §  5. 

Place  a  metal  disc  B  (Fig.  24)  under  a  light  suspended 
flat  strip  of  metal  or  needle  A,  maintained  at  a  high  positive 
potential  by  connection  with  a  highly  charged  Leyden 
jar  D.  When  the  disc  is  of  uniform  metal  the  needle  A  is 
not  deflected  to  right  or  left  by  the  presence  of  B.  A  charge 
accumulates  on  A  and  B  when  they  are  brought  close,  but 
the  charges  are  symmetrically  distributed  relatively  to  A,  so 
that  A  is  simply  attracted  to  B  and  does  not  tend  to  turn 
round  on  the  axis  or  suspending  wire  E.  But  if  the  disc  B 


Fig.  24. 

be  made  of  two  metals,  such  as  zinc  and  copper,  with  their 
junction  placed  under  the  needle  A,  this  needle  no  longer 
remains  in  equilibrium,  but  deflects  towards  the  side  on 
which  the  copper  is  placed,  showing  that  now  the  charge  on 
B  is  not  symmetrically  distributed,  but  that  there  is  a  greater 
induced  charge  on  the  copper  than  on  the  zinc.  This 
can  only  be  due  to  the  fact  that  there  is  a  greater 
difference  of  potential  between  the  needle  and  the  copper 
than  between  the  needle  and  the  zinc  ;  in  other  words,  there 
is  a  difference  of  potential  due  to  contact  between  the  zinc 
and  copper,  the  zinc  being  positive  relatively  to  the  copper. 
If  the  potential  of  A  be  negative  instead  of  positive  the 
deflection  will  be  in  the  opposite  direction.  The  two  half 
discs  may  be  separated  from  one  another  by  a  narrow  open- 
ing as  in  Fig.  25.  The  needle  will  not  deflect  if  the  two 
halves  are  of  the  same  metal.  It  will  deflect  to  a  definite 
amount  if  the  discs  are  of  different  metals  but  in  metallic 


CHAP.  II.] 


Potential 


47 


connection  by  a  wire,  and  the  deflection  d  will,  when  A  is 
positive,  be  as  before  from  the  zinc  to  the  copper,  if  these 
are  the  metals  employed  for  B  and  BJ.  In  making  this 
experiment  care  must  be  taken  to  ensure  that  the  half  discs 
are  symmetrically  placed  on  the  two  sides  of  A,  otherwise 
deflections  occur  due  to  charges  induced  on  the  two  sides 
of  A  even  when  B  and  Bt  are  at  one  potential.  If  when  the 
potential  of  A  is  reversed,  being  made  alternately  +  and  —  to 
equal  amounts,  we  obtain  equal  deflections  in  opposite  direc- 
tions, we  may  be  certain  that  this  symmetry  is  attained. 
FIG.  25. 


Let  two  such  half  discs  of  copper  be  carefully  adjusted 
under  A;  when  these  are  joined  by  metallic  contact  there 
should  be  no  deflection  however  high  the  potential  of  A  may 
be.  Then  connect  the  side  B  with  the  copper  pole  of  a  gal- 
vanic cell,  and  the  side  B!  with  the  zinc  pole  (Fig.  25);  the 
needle  A  will  deflect  towards  the  side  BJ  which  is  in  connec- 
tion with  the  zinc  pole,  and  the  amount  of  the  deflection  will 
correspond  to  the  same  difference  of  potential  as  that 
already  observed  as  due  to  the  simple  contact  of  zinc  and 
copper.  Remark  that,  whereas  in  Fig.  24  A  was  attracted  to 
the  copper  half  disc,  it  is  in  Fig.  25  attracted  to  the  half 
disc  in  connection  with  the  zinc.  We  know  from  the  first 
experiment  that  the  junction  m  has  made  the  zinc  in  the 
water  positive  and  the  copper  above  m  with  the  half  disc  Bt 
negative.  We  find  that  the  copper  c  and  the  half  disc  B  are 
positive  to  just  the  same  extent  as  z  must  be,  and  therefore 


48  Electricity  and  Magnetism.          [CHAP.  II. 

conclude  that  the  water  has  simply  brought  the  copper  strip 
and  disc  B  to  the  potential  of  the  zinc.  The  experiment  is 
a  delicate  one,  and  does  not  prove  that  the  difference  of 
potentials  between  B  and  B!  is  exactly  equal  to  that  pro- 
duced by  the  simple  metallic  contact  of  zinc  and  copper ; 
there  is  a  slight  difference  due  to  the  liquid,  and  different 
liquids  will  certainly  augment  or  decrease  this  small  dif- 
ference. Another  experiment,  hitherto  unpublished,  still 
more  strikingly  illustrates  the  Voltaic  theory.  When  the 
two  half  discs  of  copper  and  zinc  (Fig.  24)  are  connected 
by  a  metallic  wire  it  is  impossible  to  find  any  position  of 
A  such  that  a  reversal  of  its  potential  does  not  cause  a  de- 
flection, and  if  A  is  in  a  symmetrical  position  relatively  to  those 
discs  a  reversal  of  the  potential  of  A  will  always  give  equal 
deflections  to  right  or  left.  When  this  symmetrical  position 
has  been  found,  connect  the  zinc  and  copper  by  a  drop  of 
water  instead  of  by  the  metallic  wire.  The  needle  A  will 
remain  undeflected  in  its  central  position  whether  its  poten- 
tial be  high  or  low,  positive  or  negative.  The  two  half  discs 
of  different  metals  behave  as  if  they  were  of  one  and  the 
same  metal  in  metallic  connection.  This  experiment,  which 
has  been  carefully  made  by  Sir  William  Thomson,  appears  to 
be  absolutely  conclusive.  The  surface  of  the  metals  should 
be  polished  and  clean,  for  the  experiment  will  not  succeed 
if  they  are  tarnished.  Oxides  on  the  surface  of  the  metals 
introduce  complex  actions. 

The  popular  belief  that  the  zinc  and  copper  of  a  galvanic 
cell  differ  in  potential  by  an  amount  corresponding  to  the 
whole  electromotive  force  (vide  §  23)  of  the  cell,  is  then 
erroneous,  but  this  erroneous  conception  has  led  to  no  errors 
in  practice  because  the  copper,  brass,  or  other  wires  attached 
to  the  two  metals  in  the  cell  really  do  differ  in  potential  by 
the  amount  erroneously  attributed  to  the  immersed  plates. 

§  23.  The  property  of  producing  a  difference  of  potential 
may  be  said  to  be  due  to  a  peculiar  force,  to  which  force 
the  name  of  electromotive  force  is  given.  When  we  say 
that  zinc  and  water  produce  a  definite  electromotive  force, 


CHAP.  II.]  Potential.  49 

we  mean  that  by  their  contact  a  certain  definite  difference 
of  potentials  is  produced.  A  series  of  the  galvanic  batteries 
or  cells  (Chapter  I.  §  16)  produces  a  definite  electromotive 
force  between  the  terminal  metals  plunged  in  the  solution 
which  depends,  according  to  the  law  stated  above,  on  the 
successive  difference  of  potential  produced  between  each 
successive  material  at  their  surfaces  of  separation.  The 
electromotive  force  of  a  cell  or  the  difference  of  potentials 
between  the  metal  poles  or  electrodes,  as  they  are  often 
called,  is  constant  so  long  as  constant  metals  and  a  constant 
solution  are  used.  The  words  electromotive  force  and  diffe- 
rence of  potential  are  used  frequently  one  for  the  other,  but 
they  are  not  strictly  speaking  identical.  It  must  be  remem- 
bered that  electromotive  force  is  not  a  mechanical  force 
tending  to  set  a  mass  in  motion,  but  a  name  given  to  the 
supposed  force  which  causes  or  tends  to  cause  a  transfer  of 
electricity.  Wherever  difference  of  potential  is  found  there 
must  therefore  be  an  electromotive  force  ;  but  we  shall  find 
(Chapter  III.  §  22)  that  there  are  cases  in  which  electricity 
is  set  in  motion,  from  one  point  to  another,  between  which 
that  difference  of  condition  does  not  exist  which  we  have 
defined  as  difference  of  potential.  Electromotive  force  is 
therefore  the  more  general  term  of  the  two,  and  includes 
difference  of  potential  as  one  of  its  forms. 

§  24.  The  electromotive  force  exerted  between  two  dis- 
similar metals  is  altered  by  every  change  in  their  temperatures, 
but  the  connection  between  the  change  of  temperatures  and 
the  change  of  electromotive  force  has  not  been  thoroughly 
investigated.  Two  parts  of  one  and  the  same  body  at 
different  temperatures  are  probably  always  at  different 
potentials.  This  has  been  verified  only  in  certain  cases,  as 
in  the  crystals  of  tourmaline. 

§  25.  Electromotive  force  may  also  be  produced  by 
electricity  in  motion,  and  by  magnetism  in  ways  which  we 
cannot  even  describe,  until  the  simpler  phenomena  of 
electricity  in  motion  and  of  magnetism  have  been  described; 

E 


5O  Electricity  and  Magnetis m.          [CHAP.   IT. 

but  it  may  be  said  generally  that  all  causes  which  have  the 
power  of  altering  the  distribution  of  electricity  can  produce 
electromotive  force  or  difference  of  potential.  Every  source 
of  electricity  must  as  such  be  able  to  produce  a  difference  of 
potential ;  since  no  charge  of  electricity  whatever  can  be 
made  sensible  without  some  difference  of  potentials  between 
the  charged  body  and  the  earth  or  neighbouring  con- 
ductors. Friction  between  insulators  is  found  to  produce 
a  great  electromotive  force,  producing  a  large  charge  on 
even  a  small  conductor,  whereas  the  galvanic  cell  or  the 
contact  of  conductors  produces  a  very  small  electromotive 
force,  giving  a  small  charge  only  i'f  the  conductor  be  small. 
On  the  other  hand,  when  the  conductor  is  large  the  gal- 
vanic cell  will  almost  instantaneously  charge  the  whole  to  the 
maximum  potential  it  can  produce,  developing  by  chemical 
reaction  an  immense  quantity  of  electricity ;  whereas  the 
quantity  developed  by  friction  from  the  contact  of  insulators 
is  so  small  that  if  it  be  allowed  to  diffuse  itself  over  a  large 
conductor  the  potential  of  the  conductor  will  be  very  little 
raised.  For  instance,  if  we  connect  a  brass  ball  of  a  few 
inches  diameter  with  the  conductor  of  a  factional  machine, 
a  few  turns  of  the  machine  raise  its  potential  so  much  that 
its  mere  approach  to  the  knob  of  an  electroscope  will  cause 
the  gold  leaves  to  diverge.  If  we  touch  the  same  ball  with 
one  electrode  of  a  galvanic  cell,  the  other  being  connected 
with  earth,  the  brass  ball  will  indeed  receive  a  charge,  but  its 
quantity  will  be  so  small  and  its  potential  so  low  that  instru- 
ments to  detect  it  must  be  perhaps  a  thousand  times  more  sen- 
sitive than  any  I  have  yet  described.  But  if  we  connect  the 
conductor  of  a  very  large  condenser  or  Leyden  jar  with  the 
galvanic  cell,  we  shall  communicate  to  it  such  a  charge  that 
although  its  potential  would  be  insensible  on  the  electro- 
scopes hitherto  described,  its  quantity  is  such  that  it  would 
sensibly  heat  a  wire  in  its  escape  to  earth,  and  would  produce 
many  other  effects  which  could  not  be  obtained  without 
the  greatest  difficulty  from  the  same  Leyden  jar  charged  by 


CHAP.  11.]  Potential  51 

a  fractional  machine.  A  frictional  machine  charges  a  small 
Leyden  jar  with  a  much  greater  charge  than  could  be  obtained 
in  the  same  jar  even  from  1000  galvanic  cells  ranged  in  series 
as  in  §  16. 

§  26.  Difference  of  potential  or  electromotive  force  must 
be  measured  in  terms  of  some  unit  adapted  to  measure 
work.  Every  unit  of  work  must  be  represented  by  the 
operation  of  a  force  overcoming  a  resistance  so  as  to  move  it 
through  a  distance  ;  or,  what  is  the  same,  it  may  be  repre- 
sented by  the  resistance  overcome  and  moved  through  a  dis- 
tance. In  other  words,  the  unit  of  force  exerted  through  the 
unit  of  space  is  the  unit  of  work.  The  most  common  unit 
of  work  is  the  foot-pound,  being  the  weight  of  a  pound  over- 
come so  as  to  be  lifted  through  the  distance  of  a  foot,  but 
the  so-called  absolute  unit  of  work  is  that  which  leads  to 
greatest  simplicity  in  electrical  calculations.  This  unit  is  the 
absolute  unit  of  force  (Chapter  I.  §  1 7)  overcoming  a  resist- 
ance through  the  unit  distance,  say  one  centimetre.  The 
absolute  unit  of  work  (centimetre,  gramme,  second)  is  equal 
to  the  foot-pound  divided  by  13,825  g,  where  £•  is  the  velocity 
acquired  at  the  end  of  one  second  by  a  body  falling  in  vacuo  : 
taking  this  as  981  centimetres  per  second  the  absolute  unit 
of  work  is  equal  to  the  foot-pound  divided  by  13,562,325. 
The  unit  difference  of  potential  or  electromotive  force  in 
electrostatic  measure  exists  between  two  points  when  the 
unit  quantity  of  electricity  in  passing  from  one  to  the  other 
will  do  the  unit  amount  of  work. 

The  practical  measurement  of  the  difference  of  potentials 
between  two  points  can  in  certain  cases  be  made  by  observing 
the  work  done  by  definite  quantities  of  electricity  in  passing 
from  one  point  to  the  other ;  thus  we  may  observe  the  total 
amount  of  heat  generated  in  a  wire  by  a  given  quantity  of 
electricity  passing  between  two  points  kept  at  a  constant 
difference  of  potentials.  From  the  heat  we  may  calculate 
the  work,  and  from  the  heat  and  quantity  we  may  calculate 
the  difference  of  potentials.  [Similarly,  if  we  wished  to 

E  2 


52  Electricity  and  Magnetism.         [CHAP.  in. 

ascertain  the  difference  of  level  between  two  points  we  might 
let  a  weight  (a  standard  quantity  of  matter)  fall  from  one  to 
the  other,  measure  the  total  heat  generated  by  the  concus- 
sion which  brought  the  weight  to  rest,  from  the  heat  deduce 
the  amount  of  work  done,  and  from  this  work  and  the  known 
quantity  of  matter,  deduce  the  difference  of  level  or  of 
gravitation  potential.  Fortunately  there  are  more  direct 
methods  available  or  engineers  would  have  some  difficulty  in 
levelling.] 

Difference  of  electric  potentials  is  more  generally  ascer- 
tained indirectly  by  a  knowledge  of  the  laws  connecting 
potential  with  other  electrical  magnitudes.  Thus  we  know  that 
the  quantity  of  electricity  with  which  two  opposing  surfaces 
•of  conductors  are  charged  is  simply  proportional  to  the 
difference  of  potential  between  them,  assuming  the  distance 
and  dielectric  to  remain  constant.  Electrometers  afford  us 
the  means  of  comparing  such  quantities  as  these,  and  there- 
fore electrometers  (as  shown  in  §  16)  afford  us  the  means 
of  comparing  differences  of  potential.  The  measurement 
of  -currents  and  of  resistances  to  be  described  in  the  follow- 
ing chapters  give  other  means  of  comparing  differences  of 
potential. 


CHAPTER   III. 

CURRENT. 

§  1.  Electricity  has  already  been  frequently  spoken  of  as  re- 
distributing itself  over  a  given  conductor,  or  moving  from  one 
conductor  to  another  along  a  wire,  and  we  may  with  propriety 
speak  of  the  current  of  electricity  by  which  the  redistribution 
is  effected.  Bodies  along  which  electricity  moves  acquire, 
so  long  as  the  motion  lasts,  very  singular  properties,  and  in 
order  to  avoid  cumbrous  phraseology  the  properties  which 
are  actually  observed  as  belonging  to  the  bodies  through 
which  a  current  of  electricity  flows,  are  spoken  of  as  the 
attributes  of  the  current  of  electricity  itself.  Some  of  the 


CHAP.  III.]  Current.  53 

properties  of  electric  currents  are  most  conveniently  observed 
in  long  uniform  conductors,  such  as  wires,  along  which  the 
flow  takes  place  in  one  simple  direction.  Currents  in  wires 
will  chiefly  be  spoken  of  in  the  first  instance,  although 
identical  properties  are  possessed  by  currents  moving  in  any 
manner  through  bodies  of  any  form.  The  direction  of  a 
current  is  assumed  as  the  direction  from  the  place  of  high 
potential  to  the  place  of  low  potential;  in  other  words,  it  is 
the  direction  in  which  positive  electricity  flows.  Thus, 
to  recur  to  our  earliest  definition  of  positive  and  negative 
electricity,  if  one  conductor  A  be  electrified  by  contact 
with  a  stick  of  glass  which  has  been  rubbed  with  a  resinous 
material,  and  another  conductor  B  be  electrified  by  contact 
with  the  resin  used  to  rub  the  glass,  then  upon  joining  A 
and  B,  a  current  of  positive  or  vitreous  electricity  will  flow 
from  A  to  B  until  they  are  brought  to  the  same  potential. 
By  using  two  large  conductors  A  and  B,  or  two  Leyden  jars 
of  large  capacity,  and  electrifying  them  with  a  frictional 
electrical  machine  of  considerable  size  to  a  high  potential,  a 
considerable  quantity  of  electricity  may  be  accumulated  on 
A  and  B,  and  a  considerable  current  will  flow  from  A  to  B, 
when  they  are  joined. 

§  2.  A  current  of  electricity  thus  produced  will  be  transient, 
and  even  while  it  lasts  it  will  not  remain  con- 
stant, for  during  its  continuance  the  difference 
of  potentials  producing   it  will    continually 
diminish  ;  indeed,  if  the  above  were  the  only 
manner  of  producing  an  electric  current,  we 
might  still  be  ignorant  of  its  peculiar  proper- 
ties.    When  plates  of  zinc  and  copper  not 
touching  one  another  are  plunged  in  water 
and  the  copper  is  then  joined  to  the  zinc  by 
a  wire  outside  the  water,  a  current  flows  from  the  copper  to 
the  zinc  along  the  wire,  and  from  the  zinc  to  the  copper 
through  the  water.     According  to  the  theory  of  the  cell 
explained  in  the  last  chapter,  the  zinc  when    it  touched 
the  copper  became  positive  and  the  copper  negative,  the 


54  Electricity  and  Magnetism,         [CHAP.  III. 

electricities  being  separated  at  the  metallic  junction,  but 
there- being  no  opposition  to  their  recombining  through  the 
water,  the  current  flows  in  the  direction  shown.  The  exis- 
tence of  the  current  is  shown  by  the  fact  that  if  A  and  B 
be  joined  by  a  long  copper  wire,  this  wire  acquires  the  same 
properties  as  if  it  joined  two  large  conductors  charged  with 
opposite  kinds  of  electricity.  These  properties  are  described 
in  §  6  and  the  rest  of  this  chapter. 

§  3.  The  transfer  of  electricity  from  A  to  B  involves  the 
performance  of  work  or  its  equivalent,  and  to  perform  work 
implies  a  source  of  power,  or  in  other  language  an  expenditure 
of  energy.  The  mere  contact  of  two  dissimilar  substances 
cannot  be  a  source  of  power.  It  is  found  that  while  the 
current  flows  the  water  is  decomposed,  and  oxide  of  zinc 
formed.  This  chemical  reaction  is  a  true  source  of  power  ; 
the  oxygen  leaves  the  hydrogen  of  the  water  to  join  with 
the  zinc,  for  which  it  has  a  greater  affinity.  The  zinc  is 
consumed  in  the  process,  as  coal  is  consumed  when  it  burns 
while  combining  with  the  oxygen  of  the  air.  The  source 
of  power  is  accurately  described  by  saying  :  the  intrinsic 
energy  of  a  given  weight  of  zinc  and  water  is  greater  than 
that  of  the  hydrogen  gas  and  oxide  of  zinc  produced  by  the 
combination,  the  difference  is  equal  to  the  work  done  by 
the  current  of  electricity  produced.  The  work  done  by  the 
current  is  therefore  proportional  to  the  amount  of  zinc  con- 
sumed. The  electromotive  force  of  the  cell  is  constant, 
depending  on  the  substances  in  contact;  the  performance  of 
a  given  amount  of  work  by  the  transfer  of  electricity  from 
one  point  to  another,  between  which  there  is  a  constant 
difference  of  potentials  or  electromotive  force,  requires  the 
transfer  of  a  definite  amount  of  electricity,  hence  the  quan- 
tity of  electricity  produced  by  the  galvanic  cell  is  propor- 
tional to  the  zinc  consumed.  The  effect  described  as  oc- 
curring in  the  simple  form  of  the  galvanic  cell  is  produced 
whenever  we  join  two  solid  conductors  A  and  B  plunged 
in  a  compound  liquid,  one  element  of  which  tends  to 


CHAP.  III.]  Current.  55 

combine  more  strongly  with  A  than  with  B,  or  with  B  than 
with  A. 

If  we  consider  the  liquid  alone  we  find  that  positive  elec- 
tricity is  produced  apparently  at  the  surface  of  contact 
between  the  liquid  and  one  conductor,  and  is  taken  away 
as  fast  as:  it  is  produced  to  neutralise  the  negative  electricity 
produced  apparently  at  the  surface,  where  the  other  conductor 
touches  the  liquid. 

§  4.  A  bitter  war  raged  for  a  long  time  between  the  electri- 
cians who  maintained  that  in  this  case  the  electricity  was 
due  to  contact,  and  those  who  maintained  that  it  was  due 
to  chemical  action  ;  like  many  other  disputes,  it  turns  much 
upon  the  use  of.  words.1  Both  contact  between  dissimilar 
substances  and  chemical  action  are  necessary  to  produce 
the  effect ;  the  laws  regulating  the  potential  and  those  re- 
gulating the  current  are  intimately  connected  with  the 
nature  of  the  substances  in  contact,  and  with  the  amount  of 
chemical  action.  Perhaps  it  is  strictly  accurate  to  say  that 
difference  of  potential  is  produced  by  contact,  and  that 
the  current  which  is  maintained  by  it  is  produced  by  chemi- 
cal action.  As  we  shall  see  hereafter,  the  difference  of 
potentials  can  be  accurately  determined  from  a  considera- 
tion of  the  chemical  action,  but  then  this  chemical  action 
depends  probably  on  the  very  properties  which  cause  a 
difference  of  potential  to  be  produced  by  contact.  In 
cases  where  no  known  chemical  action  occurs,  as  where 
copper  and  zinc  touch  one  another,  the  difference  of  po- 
tential is  produced,  and  since  this  involves  a  redistribution- 
of  electricity,  a  small  but  definite  consumption  of  energy 
must  then  occur;  the  source  of  this  power  cannot  yet  be 
said  to  be  known. 

§  5.  The  law  described  in  Chapter  II.  §  21,  by  giving  a  con- 
tact potential  series,  or  electromotive  series,  for  metals,  shows 

1  The  opponents  of  contact  electricity  denied  and  falsely  explained 
things  now  known  to  be  true,  and  the  original  supporters  of  the  contact 
theory  were  ignorant  of  dynamics. 


56  Electricity  and  Magnetism.         [CHAP.  III. 

why  we  have  no  hope  ever  to  obtain  a  permanent  current  by 
any  arrangement  of  metals,  each  at  one  temperature.     The 
electromotive  force  at  the  joint  c  (Fig.   27)   is  necessarily 
equal  to  that  at  joint  D,  and  opposed 
to  it,  i.e.  the  E.  M.  F.  (as  electromotive 
force  may  for  brevity  be  written)  at  c 
tends  to  send  the  electricity  round  in 
the  direction  opposed  to  the  hands  of 
a  watch,  while  the  E.  M.  F.  at  D  tends 
to  send  electricity  round  in  the  opposite 
direction,  and  the  two  forces  being  equal,  electricity  moves 
neither  way. 

When  instead  of  bringing  the  zinc  and  copper  into  contact 
at  D  they  are  plunged  into  water,  the  E.  M.  F.  at  the  junction 
remains  as  before ;  but  owing  apparently  to  the  electrolysis 
or  decomposition  of  the  water,  the  electromotive  forces 
manifested  at  the  surfaces  where  the  water  touches  the 
metals  do  not  balance  that  due  to  the  contact  of  the  metals, 
and  the  current  can  therefore  flow  as  described  in  §  2.  The 
arrangement  of  potentials  in  the  cell,  in  the  plates,  and  in 
the  wire  joining  the  plates,  cannot  be  explained  until  after 
Chapter  IV.  What  chiefly  concerns  us  is  that  galvanic  cells 
can  be  arranged  so  as  to  produce  a  permanent  current 
conveying  considerable  quantities  of  electricity ;  the  strength 
of  the  current  is  simply  proportional  to  the  quantity  conveyed 
in  a  given  time. 

§  6.  The  properties  of  electric  currents  are  very  impor- 
tant. Two  parallel  wires  in  which  electric  currents  flow  in 
the  same  direction,  attract  one  another  It  is  simpler  to 
state  this  fact  by  saying  that  parallel  currents  in  the  same 
direction  attract  one  another.  Parallel  currents  in  opposite 
directions  repel  one  another. 

When  the  wires  conveying  the  currents  are  straight  but  not 
parallel,  they  attract  one  another  if  both  currents  flow  to  or 
from  the  apex  of  the  acute  angle  which  the  wires  make  with 
one  another. 


CHAP.  III.] 


Current. 


57 


The  wires  or  currents  repel  one  another  if  one  current 
approaches  and  the  other  recedes  from  the  apex  of  the  angle. 

§  7.  Consider  a  rectangle  of  wire  E  F  G  H  (Fig.  28)  held  over 
a  straight  wire  A  B,  each  having  currents  circulating  in  them, 
as  shown  by  the  arrows,  and  let  the  rectangle  be  capable  of 
turning  on  a  vertical  axis  x  xt ;  it  is  found  by  experiment  that 
E  G  is  attracted  towards  A  ;  F  H,  on  the  contrary,  towards  B  ; 
both  therefore  tend  to  turn  the  rectangle  in  the  same  direction 
round  its  axis  ;  that  portion  of  H  G  which  is  behind  A  B 
is  attracted  towards  B,  and  repelled  from  A  by  §  6.  On 
the  contrary,  the  portion  of  H  G  which  is  in  front  of  A  B 
is  repelled  from  B  and  attracted  towards  A  ;  all  these  forces 
act  therefore  in  one  direction,  and  tend  to  place  E  F  G  H  in 


FIG. 


a  plane  parallel  to  A  B.  The  forces  in  E  F  are  acting  in  the 
opposite  direction,  but  E  F  being  farther  from  A  B  than  the 
other  portions  of  the  current,  the  forces  due  to  it  are  weakei 
and  are  overpowered.  These  attractions  and  repulsions  are 
easily  verified  with  a  rectangle  of  copper  wire  made  as  in 
Fig.  29,  and  supported  by  two  pivots  a  and  b  resting  in  two 
mercury  cups,  which  are  connected  by  thick  wires  with  a 
Grove's  cell. 

§  8.  If  we  conceive  one  rectangle  A  B  c  D  (Fig.  30)  inside 
another  E  F  G  H,  all  the  actions  described  in  the  last  will  be 
strengthened,  and  the  two  rectangles  will  tend  to  place 
themselves  in  parallel  planes,  and  moreover  in  such  a  posi- 
tion that  the  current  is  going  in  the  same  direction  in  both 


5 8  Electricity  and  Magnetism.         [CHAP.  III. 

rectangles.  The  truth  of  this  proposition  is  evidently  not 
limited  to  rectangular  systems,  and  generally  any  two 
closed  wire  circuits  in  which  currents  are 
flowing  tend  to  arrange  themselves  in 
this  manner.  When  the  two  are  in  the 
same  plane  they  may  be  so  arranged,  a? 

IV^^H3  1*  f°r  instance  where  they  are  concentric 
I  J  ^^G  II  circles,  that  the  one  does  not  attract  the 
other  at  all  but  merely  directs  it,  as  de- 
scribed above.  If  the  one  circuit  were  not 
in  the  same  plane  as  the  other  they  would 
attract  one  another  even  after  they  had  placed  themselves 
in  parallel  planes,  and  if  forced  to  remain  in  such  a  position 
that  the  currents  were  flowing  in  opposite  directions  in  the 
two  circuits,  they  would  repel  one  another.  If  the  two 
circuits  were  in  one  plane,  but  not  concentric,  there  might 
be  a  resultant  force  tending  to  cause  relative  movement  in 
that  plane,  due  to  the  greater  proximity  of  the  wires  at 
certain  parts.  All  these  attractions  and  repulsions  are 
wholly  distinct  from  the  attractions  and  repulsions  between 
charges  of  electricity  at  rest.  They  were  discovered  by 
Ampere. 

§  9.  All  the  actions  of  currents  one  upon  another  may 
obviously  be  multiplied  by  using,  instead  of  a  single  wire,  a 
coil  of  wires,  through  each  winding  or  turn  of  which  the  same 
current  is  flowing.  Thus,  a  circuit  composed  of  twenty  turns 
of  wire  on  a  reel  would  be  acted  upon  with  twenty  times  the 
force  that  a  single  turn  would  experience  with  the  same  current 
flowing  through  it ;  and  again,  if  the  second  circuit  be  also 
composed  of  twenty  wires,  each  with  a  current  equal  to  the 
original  one,  the  forces  in  action  will  be  again  multiplied 
twentyfold.  So  that  a  circular  coil  A  (Fig.  3 1)  of  twenty  turns 
of  wire  hung  up  by  a  fibre  inside  a  fixed  coil  B  of  twenty 
turns  of  wire,  will  experience  a  directing  force  400  times 
greater  for  any  given  current  circulating  in  both  than  would 
be  experienced  by  a  coil  with  a  single  turn  hung  inside  a 


CHAP.  III.]  Current.  59 

coil  with  only  one  turn.     This  fact  allows  the  construction 

of  instruments  called  electro-dynamometers,  adapted  to  show 

the  presence  of  electric  currents.    A  coil  A  of 

perhaps  several  thousand  turns  may  be  hung 

up  inside  a  coil  B,  also  consisting  of  a  large 

number  of  turns,  each  turn  being  insulated 

from  its  neighbours  by  silk.     A  and  B  are, 

when  no  current  is  passing,  maintained  in 

planes   at   right  angles  to  one  another  by  a 

small  directing  force,  such  as  the  torsion  of 

a  wire.     When  a  current  is  passed  through  both,  the  inner 

coil  is  turned  in  such  a  direction  as  to  place  it  more  parallel 

to  B  than  before,  and  with  the  currents  running  in  the  same 

direction.      The   instrument   may  be   modified,  so  that  a 

known  current  is  passing  through  A,  and  the  one  to  be 

examined  passed  through  B   only.      The   direction  of  the 

unknown  current  is  indicated  by  the  direction  in  which  A 

turns,  and  its  magnitude  or  strength  by  the  angle  through 

which  it  is  turned. 

§  10.  Other  arrangements  of  a  similar  kind  will  suggest 
themselves  to  the  reader.  If  the  centre  coil  A,  instead  of 
resembling  a  ring,  were  a  coil  of  small  diameter  as  in  Fig.  32, 
forming  a  cylinder  of  considerable  length, 
so  arranged  that  the  current  flowed  in  the 
same  direction  round  all  parts  of  the  cylin- 
der, the  deflection  of  the  internal  cylinder  

would  be  more  immediately  visible,  and 
the  ends  a  and  b  might  be  considered  as  two  poles,  having 
a  tendency  to  place  themselves  at  right  angles  to  the  plane 
of  the  directing  coil.  When  such  a  cylinder  as  this  is  placed 
wholly  inside  another,  having  similar  coils  parallel  to  it, 
it  will  be  in  stable  or  unstable  equilibrium,  as  the  currents 
flow  in  the  same  or  in  opposite  directions. 

If  the  pole  a  were  introduced  inside  the  coil  B  A,  as 
shown  in  Fig.  33,  the  coil  a  would  be  sucked  in  by  the  action 
of  one  current  on  the  other.  If.  on  the  other  hand,  the 


6o 


Electricity  and  Magnetism.        [CHAP.  in. 


currents  flowed  in  such  a  direction  that  the  pole  b  were  placed 
inside  or  near  the  similar  pole  B,  as  in  Fig.  34,  the  inner  coil 
would  be  expelled  or  repelled  from  B.  These  actions  are 
apparent  whatever  be  the  diameter  of  the  coils.  Conceive 
next  that  two  flat  spiral  coils  (Fig.  35)  are  placed  face  to 
face  :  if  the  currents  flow  in  the  same  direction,  they  will 
attract  one  another;  if  in  opposite  directions,  they  will  repel 
one  another. 

Any  of  these  arrangements  may  be  made  use  of  to  show 


FIG.  33- 


FIG.  35. 


FIG.  34. 


the  presence,  direction,  and  magnitude  of  a  cunent  in  a 
wire.  By  using  a  large  number  of  turns  of  fine  copper  wire 
insulated  with  silk,  and  suspended  so  as  to  turn  with  very 
small  frictional  or  torsional  resistance,  it  is  easy  to  construct 
apparatus  showing  all  the  phenomena  described  in  §  9  and 
§  10.  The  long  cylindrical  coil  described  in  this  section  is 
sometimes  called  a  solenoid. 

§  11.  Magnets  are  found  to  be  influenced  by  electric 
currents  almost  exactly  as  solenoids  are.  In  the  presence 
of  a  current,  they  are  directed  so  that  if  free  to  move, 
they  stand  across  the  current.  This  fact  was  first  observed 
by  Oersted.  The  end  of  the  magnet  which  points  to  the 


CHAP.  III.] 


Current. 


61 


south,  when  freely  suspended,  is  similar  to  that  pole  of  the 
solenoid  in  which  the  current  is  moving  in  the  direction 
of  the  hands  of  a  watch,  holding  the  watch  with  its  back 
to  the  coil ;  or,  in  other  words,  if  the  solenoid  be  like  a 
right-handed  corkscrew  and  the  current  enters  at  the  point, 
the  point  will  behave  like  the  end  of  a  magnet  which  points 
south.  The  solenoid  and  magnet  have  many  properties  in 
common.  The  solenoid  may  be  directed  by  a  single  rec- 
tilinear current,  and  so  may  the  magnet;  but  just  as  the 
directive  action  on  the  solenoid  is  increased  by  wrapping 
the  directing  coil  all  round  it,  by  bringing  the  coils  into 
close  proximity,  and  by  increasing  the  magnitude  of  the 
current  flowing  through  the  directing  coil,  so  the  directing 
force  or  couple  acting  on  a  magnet  is  greatly  increased 
by  sending  the  current  in  the  directing  coil  round  it  many 
times,  by  bringing  that  coil  very  close  to  the  magnet,  and  by 
using  a  powerful  current.  This  property  of  the  magnet 
allows  us  to  construct  instruments  called  galvanoscopes 
and  galvanometers  for  the  detection  and  measurement  of 
currents  without  using  a  double  coil  of  insulated  wire.  In 
galvanoscopes  a  magnet  hangs  inside  a  directing  coil,  each 
turn  of  which  is  placed  north  and  south.  The  magnet  hangs 
with  its  poles  north  and  south 
so  long  as  no  current  passes 
through  the  coil,  but  when  a 
current  passes,  it  is  deflected 
more  or  less  towards  one  side 

or  the  other,  until  the  couple     w 

due  to  the  directing  action  of 

the  current  is  balanced  by  the     s"" 

couple  due   to    the   directing 

action   of  the   earth.      When 

the    current   in   the   directing 

coil  (Fig.  36)  flows  from  south 

to  north  in  the  top  of  the  coil, 

the  end  of  the  magnet  which  pointed  south,  and  which  will 


FIG.  36. 


62  Electricity  and  Magnetism,  [CHAP.  in. 

hereafter  be  called  the   south   pole   of  the  magnet,  turns 
towards  the  east. 

The  direction  in  which  a  magnet  tends  to  turn  across  a 
current  may  also  be  described  as  follows.  Imagine  a  man 
lying  on  the  wire  which  conveys  the  current,  in  such  a  direc- 
tion that  the  current  was  from  his  feet  towards  his  head,  his 
face  being  turned  towards  the  magnet ;  then,  under  the  in- 
fluence of  the  current,  the  pole  of  the  magnet  which,  when 
free,  turns  to  the  south,  will  turn  towards  the  right  hand  of 
the  man.  Or  let  a  current  be  flowing  through  a  copper  cork- 
screw, and  let  the  magnet  take  up  its  natural  position  inside 
the  coils  of  wire ;  then  if  the  corkscrew  be  turned  the  way  of 
the  current  it  will  screw  from  south  to  north,  through  the 
compass  needle  considered  as  a  cork. 

The  following  is  a  third  description  of  the  direction  in 
which  a  current  deflects  a  magnet.    Imagine  a  watch  strung  on 
FlG.  37<  the  wire  conveying  a 

current  so  that  this 
current  goes  in  at  the 
back  of  the  watch 
and  comes  out  at  the 
face  through  the  cen- 
tral pivots ;  then  the 
south  pole  of  the  magnet  is  impelled  by  the  current  in  the 
direction  of  the  hands  of  the  watch  (Fig.  37). 

§  12.  Thegalvanoscope  and  galvanometer  are  instruments 
of  such  importance  that  they  will  be  described  at  length  in 
Chapter  X. ;  but  since  we  shall  have  occasion  in  future  con- 
tinually to  speak  of  electric  currents  and  their  properties,  it 
is  desirable  to  state  how  a  galvanometer  may  be  easily  con- 
structed capable  of  indicating  the  presence  of  a  current  and 
of  comparing  the  relative  strengths  of  various  currents.  Wind 
copper  wire  insulated  with  silk  on  a  hollow  brass  cylindrical 
bobbin  A  (Fig.  38)  with  deep  flanges  B  B15  which  may  have  feet 
at  c  by  which  the  bobbin  is  supported  on  wood  or  vulcanite. 
Inside  A  fit  a  small  brass  plug  D,  having  at  one  end  a  hollow 


CHAP.  III.] 


Current. 


chamber,  closed  by  the  lens  E,  with  a  focal  distance  of 
about  120  centimetres.  In  the  little  chamber  suspend  a 
mirror  and  magnet  by  a  FIG.  3s. 

single  silk  fibre,  such  as 
may  be  drawn  out  of  a 
cheap  silk  ribbon.  This 
fibre  must  be  so  thin  as  to 
be  nearly  invisible.  The 
•mirror  should  be  formed  of 
microscope  glass  as  truly 
plane  and  as  thin  as  possi- 
ble. The  magnet  may  be 
attached  to  the  back  by  a 
little  shellac  dissolved  in 
spirits  of  wine.  Care  must 
be  taken  that  the  mirror 
is  not  drawn  out  of  shape 
by  the  magnet.  The  silk 
fibre  must  also  be  attached  with  shellac  varnish.  It  may 
then  be  threaded  through  a  hole  in  the  chamber  by 
means  of  a  needle  of  sealing  wax  or  shellac,  and  secured 
with  a  little  mastic  or  other  varnish.  The  plug  D  can  then  be 
introduced  or  withdrawn  from  A  at  pleasure. 

If  currents  are  to  be  observed  which  are  passing  through 
circuits  of  great  length  or  containing  bad  conductors  the  wire 
should  be  thin,  say  No.  40,  and  many  thousand  turns  may 
be  employed  :  the  diameter  of  the  chamber  inside  the  plug  D 
maybe  1*5  centimetre,  the  length  from  B  to  BJ  3*5  centi- 
metres, and  the  outside  diameter  of  the  flanges  BBj  6  or  7 
centimetres.  This  size  will  contain  many  thousand  turns 
of  fine  wire. 

If  currents  are  to  be  observed  which  are  passing  in 
short  lengths  of  wire  or  other  good  conductors  the  space 
inside  the  flanges  B  El  may  be  filled  with  two  or  three  dozen 
turns  of  stout  copper  wire,  say  No.  16  or  No.  20.  The  two 
ends  of  this  coil  TTI  may  conveniently  be  connected  to  two 


CHAP.  III.]  Current.  65 

brass  pieces  (Fig.  39)  well  insulated  by  vulcanite  and  having 
screws  by  which  other  wires  can  be  joined  to  the  same  ter- 
minals as  they  are  called.  The  instrument  is  completed  by  a 
paraffin  lamp  L,  placed  behind  a  screen  having  a  slit  M  in 
it  about  60  centimetres  in  front  of  the  coil  and  horizontal 
white  scale  N  about  45  centimetres  long. 

When  placed  as  in  Fig.  39  the  light  from  the  lamp  passes 
through  the  slit  in  the  screen,  through  the  lens  E  on  to  the 
mirror  F,  by  which  it  is  reflected  back  on  to  the  scale. 
An  image  of  the  flame  is  seen  on  the  scale.  When  the 
light  falls  perpendicularly  on  the  mirror  this  image  appears 
on  the  scale  immediately  above  the  slit  in  the  screen.  If 
by  the  passage  of  a  current  through  the  coil  the  magnet  is 
deflected  to  the  right  or  left,  the  image  moves  to  the  right 
or  left  along  the  scale,  the  angle  formed  by  the  reflected 
rays  being  twice  the  angle  through  which  the  magnet  and 
mirror  are  deflected.  A  very  small  angle  produces  a  great 
displacement  of  the  image.  With  the  dimensions  named 
the  horizontal  displacement  of  the  image  is  nearly  propor- 
tional to  the  strength  of  the  current.  If  the  scale  be  bent 
so  as  to  form  part  of  a  cylindrical  surface  having  the  axis  of 
suspension  of  the  mirror  as  its  central  axis,  the  reflected 
spot  of  light  is  more  clearly  seen  through  the  whole  range. 
This  instrument  is  Sir  William  Thomson's  mirror  galvano- 
meter. With  its  assistance  the  presence,  increase,  or 
decrease  of  a  current  can  be  observed.  It  is  convenient 
to  place  a  bar  magnet  s  in  the  magnetic  meridian  imme- 
diately above  the  coil ;  by  raising  or  lowering  this  magnet, 
the  directive  force  of  the  earth  may  be  increased  or  weak- 
ened. If  the  south  pole  of  s  is  placed  to  the  south  the 
magnet  may  by  trial  be  put  Ut  such  a  distance  from  the 
suspended  mirror  and  magnet  as  almost  exactly  to  counter- 
balance the  effect  of  the  earth's  magnetism.  The  instru- 
ment will  then  be  very  sensitive,  but  the  spot  of  light  will  never 
remain  quite  stationary.  A  second  magnet  T,  placed  per- 
pendicular to  the  magnetic  meridian,  may  be  used  to  adjust 

F 


66  Electricity  and  Magnetism.         [CHAP.  III. 

the  zero  of  the  instrument,  i.e.  to  bring  back  the  spot  of 
light  to  a  fiducial  mark  at  the  centre  of  the  scale  when  no 
current  is  passing.  The  direction  of  the  magnetic  meridian 
is  that  in  which  a  free  magnet  naturally  points. 

§  13,  A   current  not  only  acts  on  a  piece   of  steel  or 
iron  which  is  already  a  magnet,  but  it  converts  any  piece 
of  non-magnetised  steel  or  iron  in  its  neighbourhood  into 
FlG  40  a  magnet  having  its  poles  so 

situated  that  they  lie  in  the 
_N  line  along  which  a  free  magnet 
would  place  itself  under  the 
action  of  the  current.  This 
magnetising  action  is  more 
powerful  as  the  iron  is  placed  nearer  the  current,  as  the 
current  is  more  powerful,  and  as  a  greater  length  of  the 
current  acts  in  the  same  sense  on  the  iron.  Thus,  a  piece 
of  iron  placed  inside  a  helix  or  bobbin  (Fig.  40)  of  many 
coils  is  strongly  magnetised  by  the  current  and  has  its  north 
and  south  poles  placed  as  shown  in  Fig.  40. 

The  magnetisation  produced  by  the  current  is  only  tem- 
porary if  the  iron  be  soft  or  annealed,  but  a  portion  of  the 
magnetisation  produced  in  hard  iron  is  retained  long  after 
the  current  has  ceased  to  flow,  and  in  a  hard  steel  bar  some 
portion  of  it  is  permanently  retained.  Work  is  done,  and 
energy  expended,  in  producing  this  magnetisation. 

§  14.  The  current  in  the  wire  implies  a  transfer  of  elec- 
tricity under  the  action  of  electromotive  force  ;  and  by  the 
very  definition  of  electromotive  force  work  in  some  form 
must  be  done  during  the  transfer. 

When  a  current  flows  through  a  simple  wire  and  does 
not  magnetise  iron  or  set  any  mass  in  motion,  the  energy 
expended  in  producing  the  current  is  wholly  employed 
in  heating  the  conducting  wire,  the  heat  developed  in  any 
part  of  the  wire  being  precisely  equivalent  to  the  work 
which  would  be  done  in  bringing  the  same  quantity  of 
electricity  from  the  one  end  of  the  wire  to  the  other  on  a 


CHAP.  III.] 


Current. 


67 


little  conductor  against  the  statical  repulsion  described  in  §  i, 
Chapter  II.  If  any  portion  of  the  energy  is  employed  in  other 
ways,  as  described  above,  so  much  less  heat  is  developed  in 
the  wire.  The  rise  of  temperature  in  the  wire  depends  on  the 
specific  heat  of  the  metal  of  which  it  is  composed. 

§  15.  When  the  current  traverses  a  compound  liquid 
conductor  instead  of  a  solid  simple  metal  wire,  the  liquid  is- 
in  many  cases  decomposed,  one  element  or  group  of  ele- 
ments moves  to  the  spot  at  which  the  current  enters  the 
fluid,  and  the  other  to  the  spot  at  which  the  current  leaves 
the  fluid.  Faraday  called  the  metal  surface  at  which  the 
positive  current  entered  the  fluid  the  anode,  and  the 
other  surface  the  kathode.  The  compound  decomposed 
by  the  electricity  is  called  an  electrolyte,  the  process  ot 
decomposition  electrolysis  and  the  products  of  electrolysis 
ions.  Thus  when  two  glass  tubes  (Fig.  41)  c  and  D,  filled 
with  water,  are  inverted  over  a  vessel  of  water,  and  the  two- 
platinum  wires  A  B  introduced  into  the  vessel,  then  upon- 
connecting  A  and  B  with  a  suffici- 
ently powerful  galvanic  battery  so 
that  a  current  may  pass  from  A  to  B, 
the  water  is  electrolysed ;  oxygen  is 
found  in  c  and  hydrogen  in  D,  in 
the  proportions  forming  water. 

Energy  is  expended  in  decom- 
posing any  compound,  just  as 
energy  is  evolved  in  the  combina- 
tion of  elements  which  have  a 
chemical  affinity  one  for  another. 
The  energy  expended  in  the  de- 
composition of  an  electrolyte  is  not 
available  to  produce  motion  or  heat 
in  the  circuit. 

§  16.  Currents  traverse  even  very 
bad  conductors,  but  the  current  is 
small,  i.e.  comparatively  little  electricity  passes  in  a  given 

F  2 


FIG.  41. 


68  Electricity  and  Magnetism.          [CHAP.  III. 

•time  with  a  given  E.  M.  F.  Bad  conductors  are  generally 
compound  bodies.  The  resins,  may  be  taken  as  examples. 
Feeble  currents  also  traverse  electrolytes  without  producing 
any  sensible  amount  of  electrolysis.  It  is  certain  that  work 
of  some  kind  is  done  by  the  current  as  it  passes  through 
these  bodies ;  but  it  is  not  yet  known  by  what  action  the 
work  is  represented,  that  is  to  say,  it  is  not  known  whether 
the  bad  conductor  is  heated,  or  decomposed,  or  whether 
-some  other  form  of  work  represents  the  energy  expended. 

§  17.  If  a  current  be  allowed  to  set  a  magnet  in  motion, 
for  instance,  to  expel  one  pole  of  a  magnet  previously  intro- 
duced into  a  helix,  the  current  experiences  a  real  resistance, 
and  its  flow  is  checked  by  the  effort.  The  mere  presence 
of  the  magnet  if  it  is  at  rest  does  not  check  the  current ;  a 
certain  statical  force  exists  between  the  current  and  the 
magnet,  but  so  long  as  no  motion  occurs  in  consequence  of 
this  force  or  against  this  force  no  work  is  done,  and  the 
current  flows  as  if  the  magnet  were  not  there.  A  rough 
analogy  to  this  might  be  found  in  the  following  arrangement. 
Let  water  be  flowing  through  a  pipe  at  one  side  of  which 
there  is  a  piston  A  (Fig.  42)  held 
FlG'  42'  in  position  by  a  spring  at  B.  The 

water  as  it  flows  through  the  pipe 
•,,*>,«,***  will  press  on  the  piston  A,  and  by 
means  of  a  piston-rod  may  exert  a 
force  at  B.  When  this  force  just 
balances  the  force  of  the  spring,  the 
water  in  flowing  past  the  piston  does  no  work  by  means  of  it 
or  on  it,  and  the  current  proceeds  as  if  no  piston  were  there ; 
but  if  the  spring  be  then  weakened  or  let  go  so  as  to  be  forced 
back  by  the  piston,  the  lateral  pressure  of  the  water  in 
forcing  back  the  piston  overcomes  a  resistance  through 
a  certain  space  and  does  work  as  the  current  of  electricity 
does  in  moving  the  magnet.  Moreover,  the  flow  of  water 
will  be  checked  or  diminished  while  the  work  of  pushing 
back  the  spring  is  being  done.  When  the  spring  has  been 


CHAP,  in.]  Current.  69 

pushed  back  so  far  that  its  elastic  force  balances  the  pressure 
in  the  pipe,  the  current  in  the  main  pipe  will  flow  on  as 
before,  unaffected  by  the  presence  of  the  spring  B.  In 
like  manner  the  electric  current  which  was  checked  in  its 
flow  while  deflecting  the  magnet  flows  on  as  before  after  the 
magnet  has  come  to  rest.  The  analogy  is  imperfect,  inasmuch 
as  the  diminution  of  the  water  current  is  accompanied  by  a 
change  of  capacity  for  the  water,  whereas  the  diminution  of 
the  electric  current  is  unaccompanied  by  any  increase  of 
capacity.  The  water  is  only  diverted,  whereas  the  elec- 
tricity is  really  retarded.  This  diminution  of  the  current 
while  it  is  doing  work  occurs  not  only  when  the  work  con- 
sists in  moving  a  magnet,  but  also  when  the  work  consists 
in  moving  a  wire  or  wires  conveying  currents,  as  in  the 
electro -dynamometer,  or  in  magnetising  soft  iron. 

§  18.  If  the  piston  A  in  Fig.  42  be  forced  back  towards 
the  pipe  containing  water,  it  will  produce  a  current,  the 
effect  being  reciprocal  to  that  which  was  produced  when  the 
current  was  diminished  by  forcing  forward  the  piston ;  work 
is  done  by  the  piston  as  it  is  forced  forward,  and  this  work 
is  expended  in  producing  an  extra  current  of  water. 

Similarly,  if  the  magnet  which  has  been  deflected  be 
forcibly  moved  back,  energy  is  required  to  force  it  bax:k 
against  the  resistance  due  to  the  electrical  repulsion  of  the 
current,  and  this  energy  performs  work  represented  by  an 
increase  in  the  current  exactly  corresponding  to  the  diminu- 
tion experienced  when  the  current  was  expending  energy 
in  forcing  back  the  magnet.  The  current  is  said  to  be 
induced  in  the  wire  by  the  motion  of  the  magnet  relatively 
to  the  wire.  The  case  is  one  of  energy  stored  and  restored. 
When  the  current  forced  back  the  magnet  the  energy  of  the 
current  was  expended  in  such  a  manner  as  to  be  stored  up 
in  the  system.  When  the  magnet  returns  to  its  original 
position  the  energy  is  restored  to  the  current  The  exam- 
ple already  given  of  water  in  a  pipe  forcing  back  water 
against  a  spring  affords  one  instance  of  energy  stored  and 


/O  Electricity  and  Magnetism.         [CHAP.  III. 

restored;  another  is  afforded  by  the  common  pendulum. 
The  energy  of  the  pendulum  exists  alternately  in  a  latent 
or  potential  form  due  to  the  attraction  of  gravitation, 
and  as  actual  energy  due  to  motion.  As  the  bob  rises 
the  actual  energy  is  gradually  transformed  into  potential 
energy,  being  thus  stored  up.  As  the  bob  falls  the 
potential  energy  is  reconverted  into  actual  energy,  being 
thus  restored.  Just  so,  if  a  current  deflects  a  magnet  and 
causes  it  to  swing  backwards  and  forwards,  the  energy 
alternately  exists  in  the  form  of  electric  repulsion  and 
actual  energy  of  motion;  but  there  is  this  difference  between 
electric  and  gravitation  examples  :  the  force  of  gravitation 
is  neither  increased  nor  diminished  by  the  motion  of  the 
pendulum,  whereas  when  the  magnet  swings  in  obedience 
to  the  impulse  given  by  the  current,  the  current  diminishes, 
and  when  the  magnet  swings  back  against  the  impulse  of 
the  current,  the  current  is  increased. 

§  19.  Motion  of  the  piston  in  Fig.  42  would  produce  a 
current  in  the  pipe,  whether  one  existed  before  or  not ; 
if  the  piston  were  drawn  back  from  the  pipe  it  would  suck 
water  in  at  the  mouth,  if  moved  forward  it  would  drive 
water  out ;  quite  similarly,  the  motion  of  a  magnet  in  the 
neighbourhood  of  a  conductor,  the  motion  of  a  wire  contain- 
ing an  electric  current,  or  the  increase  or  decrease  of 
magnetism  in  a  magnet  near  a  conductor,  will  each  of  them 
cause  currents  to  flow  in  that  conductor ;  the  direction  of 
the  current  in  the  conductor  or  wire  will  be  such  that  it  resists 
the  motion  of  the  magnet  or  of  the  current,  or  the  change  in  the 
current,  or  the  change  of  magnetisation. 

The  following  are  examples  of  the  application  of  this 
general  principle,  first  enunciated  by  Lenz.  Let  there  be 
a  metallic  ring  A  B  (Fig.  43),  a  second  ring  c  D,  in  which  a 
current  flows  in  the  direction  of  the  arrows,  and  a  magnet 
N  s ;  then,  while  the  relative  position  of  c  D,  A  B,  and  N  s 
do  not  vary,  and  while  the  current  in  c  D  and  the  mag- 
nstism  in  N  s  remain  constant,  neither  increasing  nor 
diminishing,  no  current  whatever  will  flow  in  the  ring  A  B, 


CHAP.  III.]  Czirrent.  71 

but  any  change  in  any  one  of  these  conditions  will  produce 
a  current  in  A  B;  thus  : 

T.  If  the  ring  c  D  moves 
nearer  A  B  a  current  will  be 
induced  in  A  B  in  the  direc- 
tion of  the  inside  arrows,  and 
during  this  action  the  current 
in  c  D  will  be  diminished. 

2.  If  the  ring  c  D  be  re- 
moved  farther   from   A   B   a 
current  will  be  induced  in  A  B 
in  the  direction  of  the  outside 

arrows,  and  during  the  induction  the  current  in  c  D  will  be 
diminished. 

3.  If  the  pole  N  of  the  magnet  N  s  be  pushed  into  the 
ring  or  nearer  to  it,  a  current  will  be  induced  in  A  B  in  the 
direction  of  the  inside  arrow,  and  the  motion  is  resisted. 

4.  If  the  pole  N  of  the  magnet  be  withdrawn  to  the  right 
hand,  out  of  or  away  from  the  ring,  a  current  will  be  induced 
in  A  B  in  the  direction  of  the  outside  arrows,  and  the  motion 
is  resisted. 

5.  If  the  magnetism  of  the  magnet  be  increased,  a  current 
will  be  induced  in  A  B  in  the  direction  of  the  inside  arrows, 
and  the  increase  of  magnetism  is  thereby  resisted. 

6.  If  the   magnetism  of  the  magnet  be   diminished,   a 
current  will  be  induced  in  A  B  in  the  direction  of  the  outside 
arrows,  and  the  diminution  of  magnetism  is  thereby  resisted- 

If  instead  of  simple  rings  we  have  long  thick  coils  of  many 
turns,  the  effects  will  be  much  more  sensible.  The  effects 
of  induction  between  straight  wires  and  magnets  can  with 
ease  be  deduced  from  the  general  principle  enunciated 
above.  Induction  is  the  name  given  to  this  phenomenon, 
which,  however,  has  nothing  in  common  with  the  induction 
described  in  Chapter  I.  To  distinguish  between  these  phe- 
nomena, that  described  in  Chapter  I.  must  be  designated 
electrostatic  induction,  and  the  induction  of  currents,  electro- 


72  Electricity  and  Magnetism.         [CHAP.  HI. 

magnetic  induction.  Electrostatic  induction  is  called  '  in- 
fluence '  in  French  and  German. 

Owing  to  electro-magnetic  induction  magnets  and  wires 
conveying  electric  currents  are  not  as  free  to  move  as  other 
bodies.  They  may  when  at  rest  be  in  perfect  equilibrium,  and 
apparently  free  to  move  in  all  directions,  but  when  we  move 
them  they  induce  currents  in  neighbouring  conductors,  and 
these  currents  are  in  such  a  direction  as  to  produce  a  force 
opposing  the  motion  of  the  first  magnet  or  current.  It  is, 
indeed,  impossible  to  conceive  that  by  moving  they  should 
produce  a  force  helping  their  own  proper  motion  as  in 
that  case  perpetual  motion,  or  rather  a  perpetually  increasing 
source  of  energy,  would  be  the  result. 

§  20,  A  current  which  commences  in  a  given  circuit  may 
be  likened,  so  far  as  its  effects  on  a  neighbouring  conductor 
are  concerned,  to  a  permanent  current  brought  suddenly 
from  an  infinite  distance  to  the  spot  where  it  stands.  We 
know  that  by  bringing  a  current  c  D  (Fig.  43)  from  a  distance 
to  a  position  alongside  a  wire  forming  part  of  a  distinct 
circuit  A  B,  we  should  cause  the  induction  of  a  current  in 
A  B  opposite  in  direction  to  that  flowing  in  the  parallel 
wire  c  D.  The  beginning  of  a  current  in  c  D  has  exactly  the 
same  effect  and  induces  a  current  in  the  opposite  direction 
in  A  B  ;  again,  an  increase  of  current  in  c  D  acts  in  the  same 
manner  as  bringing  c  D  nearer  to  A  B.  It  induces  a  current 
in  the  opposite  direction  to  that  in  c  D.  These  induced 
currents  cease  as  soon  as  the  inducing  current  c  D  ceases  to 
increase,  just  as  the  induced  current  in  A  B  would  cease  as 
soon  as  c  D,  while  conveying  a  permanent  current,  ceased 
to  approach  A  B. 

The  diminution  of  a  current  in  c  D  produces  the  same 
effect  as  removing  c  D  from  the  neighbourhood  of  A  B,  i.e.  it 
induces  a  current  in  A  B  in  the  same  direction  as  that  in  c  D. 
The  total  cessation  of  the  current  c  D  acts  like  the  infinitely 
distant  removal  of  c  D  with  its  current,  and  of  course  induces 
a  current  in  A  B  in  the  same  direction  as  that  which  flowed 


CHAP.  III.]  Current.  73 

through  c  D.     We  may  therefore  add  to  the  examples  given 
in  §  19  two  more. 

7.  If  the  current  in  c  D  ceases  or  is  diminished,  a  current 
will  be  induced  in  A  B  in  the  direction  of  the  outside  arrows, 
and  the  diminution  of  the  current  in  c  D  is  thereby  delayed. 

8.  If  the  current  in  c  D  commences  or  is  increased,  a 
current  will  be  induced  in  A  B,  in  the  direction  of  the  inside 
arrows,  and  the  increase  of  the  current  in  c  D  is  thereby 
delayed. 

§  21.  Induction  is  the  unfailing  accompaniment  of  the  be- 
ginning or  increase  and  termination  or  decrease  of  a  current, 
for  there  are  always  conductors  somewhere  near  in  which  the 
induced  currents  flow.  The  induced  currents  diminish  for 
the  time  being  the  strength  of  the  inducing  current,  and 
thus  we  see  that  neighbouring  bodies  change  the  rate  at  which 
a  beginning  or  ceasing  current  comes  to  its  permanent  con- 
dition. If  the  whole  or  a  large  part  of  a  circuit  of  small 
resistance  is  very  near  the  inducing  current,  and  so  disposed 
that  the  induction  tends  to  occur  throughout  in  one  direction, 
the  induced  current  will  be  considerable,  and  its  reaction  on 
the  inducing  current  will  also  be  great,  shortening  the  time 
it  requires  to  reach  the  permanent  condition.  If  the  circuit 
in  which  the  induced  current  flows  is,  on  the  contrary,  far 
removed  from  the  inducing  current,  or  only  exposed  to  in- 
duction for  a  small  part  of  its  length,  or  so  placed  that  the 
current  tends  to  flow  in  opposite  directions  at  different  parts 
of  the  circuit,  or  has  a  great  resistance,  then  the  induced 
current  will  be  small  and  its  reaction  on  the  inducing 
current  will  also  be  small.  The  inducing  current  produces 
an  electromotive  force  in  the  circuit  conveying  the  induced 
current,  and  we  may  say  that  the  induced  current  is  due 
to  the  induced  electromotive  force.  If  the  inducing  current 
A  be  near  a  number  of  conductors  BCD,  the  induced  current 
in  B  tends  to  weaken  that  in  c  and  D,  inasmuch  as  a  current 
beginning  in  B  would  induce  currents  in  c  and  D  in  the 
direction  of  the  original  current  A.  Thus  the  induced 


74  Electricity  and  Magnetism.         [CHAP.  III. 

current  in  B  is  less  than  it  would  have  been  if  c  and  D  had 
not  been  there,  and  the  inducing  current  in  A  is  less 
checked  than  it  would  have  been  if  c  and  D  had  not  been 
there.  , 

An  increasing  or  diminishing  current  not  only  induces  an 


FIG.  44- 

^H£ —  B 


-A 


£.  M.  F  in  neighbouring  conductors  but  also  exercises  an  in- 
ductive action  on  the  current  in  which  it  flows.  Thus  let 
us  consider  a  circuit  coiled  back  as  in 
the  annexed  figure.  An  increasing  current 
between  A  and  B,  flowing  as  shown  by  the 
arrow,  tends  to  induce  a  current  between 
C  and  D  in  the  opposite  direction.  The 
E.  M.  F  thus  induced  between  c  and  D  op- 
poses the  original  current,  and  delays  its 
increase.  If  the  current  between  A  and  B 
is  diminishing,  it  tends  to  induce  a  current 
between  c  and  D  in  the  same  direction  as  it  is  flowing,  and 
the  result  is  to  delay  the  decrease.  Thus  the  action  in  both 
cases  is  to  delay  change.  Even  when  the  wire  is  straight  a 
similar  but  much  weaker  effect  occurs.  A  current  flowing 

FIG.  46. 
A  B  C  D 


(Fig.  46)  from  A  to  B  repels  one  flowing  from  cto  D  ;  if  then  a 
current  increases  in  A  B,  it  induces  a  current  in  front  of  itself 
in  the  direction  in  which  it  is  flowing,  and  is  checked  in  so 
doing.  The  effect  is  to  diminish  the  abruptness  of  the 
increase. 

§  22.  The   conductor  in  which  the   current  is  induced 


CHAP.  III.]  '  Current.  75 

need  not  form  what  is  called  a  closed  circuit,  i.e.  such 
a  conductor  as  is  formed  by  a  ring  of  wire  round  which 
the  current  can  continue  to  flow  permanently  if  a  per- 
manent E.  M.  F.  be  kept  up  round  it,  as  distinguished  from  a 
broken  circuit,  such  as  would  be  formed  by  a  ring  of  wire 
incomplete  at  one  or  more  points,  where  the  presence  of  air 
or  other  non-conductors  would  stop  any 'permanent  current; 
but  although  the  induced  current  will  be  very  different  in 
the  two  cases  of  a  closed  and  open  circuit  it  will  be  pro- 
duced in  both.  In  the  closed  circuit  we  may  have  a  current 
induced  without  difference  of  potentials  between  the  parts. 
We  cannot  have  difference  of  potential  between  two  parts 
of  a  conductor  without  a  current  ensuing,  but  we  may  have 
a  current  due  to  E.  M.  F.  without  any  difference  of  poten- 
tial. The  analogy  of  water  in  a  pipe  will  make  this  clear. 
If  there  be  difference  of  level  between  two  reservoirs  in 
connection  with  one  another,  as  in  Fig.  47,  the  water  will 
flow  from  the  higher  level  to  the 
lower.  But  even  if  the  two  reser- 
voirs be  at  the  same  level,  when 
a  rope  is  rapidly  drawn  through 
the  pipe  from  A  to  B,  water  will 
by  friction  be  dragged  along  the  pipe,  and  water  will  flow  from 
A  to  B,  causing  B  to  rise  in  level  or  gravitation  potential. 
Here  the  current  cannot  be  said  to  be  due  to  a  difference  of 
potential,  and  the  difference  of  potential  which  finally  results 
from  the  action  is  opposed  to  that  which  would  have  pro- 
duced the  current. 

Again,  if  the  water  be  enclosed  in  a  circular  pipe  (Fig.  48), 
and  an  internal  wire  a  a  a  be  caused  to  rotate  inside  this  pipe 
about  the  axis  of  the  ring,  it  will  set  all  the  water  in  the 
pipe  in  motion,  without  causing  any  difference  of  pressure 
between  two  parts  of  the  pipe;  in  this  case  there  is  no 
difference  of  gravitation  or  pressure  potential  causing  the 
motion,  nor  is  any  difference  of  potential  necessarily  caused 
by  the  motion.  The  two  cases  of  a  closed  and  broken 


7 6  Electricity  and  Magnetism.         [CHAP.  III. 

circuit  are  analogous  to  this.  In  the  closed  circuit  the 
current  may  continue  indefinitely  so  long  as  the  motion  of 
the  inducing  magnet  continues,  but  no 
difference  of  potential  need  be  produced 
between  any  parts  of  the  circuit.  In 
the  broken  circuit,  on  the  contrary,  the 
current  is  not  produced  by  a  difference 
of  potential  between  different  parts,  but 
the  E.  M.  F.  drives  positive  electricity  to 
one  end  of  the  wire,  and  negative  electri- 
city to  the  other,  producing  a  difference  of 
potentials  which  will  send  back  a  reverse  current  so  soon  as 
the  inducing  action  of  the  magnet  is  over;  the  first  current 
may  be  exceedingly  small,  even  in  cases  where  if  the  circuit 
were  closed  the  current  would  be  great,  for  a  small  quantity 
will  in  bodies  of  small  capacity  be  quite  enough  to  produce 
a  difference  of  potential  balancing  the  inductive  action  of 
the  magnet.  Just  as  in  Fig.  47,  if  the  reservoirs  A  and  B 
are  small,  a  very  little  water  dragged  from  A  to  B  by  friction 
will  establish  such  a  difference  of  potentials  as  will  stop  all 
further  current  though  the  friction  might  be  sufficient  to 
cause  a  great  current  in  the  closed  circuit  (Fig.  48).  As 
soon  as  the  difference  of  potentials  between  A  and  B  in  the 
broken  circuit  is  sufficient  to  cause  a  reverse  current  equal 
to  that  which  the  magnet  moving  as  it  does  can  induce,  no 
further  current  will  be  induced  in  the  broken  circuit,  pre- 
cisely as  under  similar  circumstances  the  friction  of  the  rod 
would  cease  to  produce  a  current  of  water ;  but  no  motion 
of  the  magnet  or  other  inducing  system  can  be  so  small  as 
to  fail  to  produce  a  continued  current  in  the  closed  circuit, 
for  no  difference  of  potentials  is  necessarily  created  tending 
to  reverse  the  action. 

§  23,  A  complex  case  arises  when  the  closed  circuit  is 
long  and  of  sensible  capacity  while  the  inducing  action  takes 
place  on  one  part  only.  This  case  is  analogous  to  a  long 
elastic  pipe  (as  in  Fig.  49),  inside  which  a  short  rod  is 


y 


CHAP.  III.]  Current.  77 

moving,  producing  a  current  by  friction;  here  there  may 
be  accumulation  of  water  in  front  of  the  rod  and  a  deficiency 
behind.  There  may  be,  there-  FlG  4g 

fore,  an  increase  of  pressure  in 
front  of  the  rod  and  a  defect 
behind,  tending  to  reverse  the 
current  produced  by  the  fric- 
tion of  the  rod.  Just  so  with 
the  electric  current,  there  may  be  at  parts  of  the  long  circuit 
differences  of  potential  produced  tending  to  reverse  the 
direction  of  the  induced  current ;  the  potential  being  raised 
at  the  parts  into  which  the  positive  current  is  flowing,  and 
depressed  at  those  parts  from  which  it  is  flowing.  This 
implies  unequal  currents  in  different  parts  of  the  circuit. 
Examples  of  this  kind  of  action  occur  in  submarine  cables. 

§  24.  The  strength  of  a  constant  current  in  any  circuit  is 
equal  in  all  parts  of  the  circuit.  In  this  case,  although  one 
part  of  the  circuit  may  be  a  thick  wire  and  another  part  a 
thin  one,  a  third  part  an  electrolyte,  &c,,  the  quantity  of 
electricity  conveyed  past  each  section  is  the  same  in  the 
same  time,  i.e.  the  strength  of  the  current  is  the  same  at 
each  part.  Equal  lengths  of  current,  whether  conveyed 
in  a  thick  or  thin  wire,  will  produce  precisely  the  same 
effect  in  directing  magnets  and  in  producing  magnetism,  &c. 
This  equal  current  in  all  parts  of  the  circuit  is  independent 
of  the  capacity  of  each  part,  as  it  is  independent  of  the  dif- 
ference of  materials.  There  are  not  two  kinds  or  qualities  of 
current ;  a  current  has  but  the  one  quality  of  magnitude, 
meaning  that  it  conveys  a  certain  definite  quantity  of  electri- 
city past  a  given  point  in  a  given  time.  When  the  epithets 
great,  strong,  intense,  are  applied  to  currents  they  all  mean 
the  same  thing,  and  mean  that  a  large  quantity  of  electricity 
is  conveyed  by  them.  The  uniform  current  of  electricity  is 
analogous  to  the  uniform  current  of  water.  If  water  be 
flowing  from  one  reservoir  to  another  through  a  succession 
of  pipes  of  different  diameters  all  full,  the  water  will  flow  in 


78  Electricity  and  Magnetism.         [CHAP.  in. 

a  uniform  current  as  denned  above  through  all  of  them ;  that 
is  to  say,  the  same  quantity  of  water  per  second  passes 
through  every  pipe;  the  velocity  of  the  water  is  different 
wherever  the  diameters  of  the  pipes  differ;  but  the  current 
is  constant  in  the  sense  that  it  is  a  current  of  so  many 
gallons  per  second.  When  a  good  form  of  voltaic  battery  is 
used  to  produce  the  difference  of  potentials,  and  the  current 
is  allowed  to  flow  through  a  metallic  conductor,  kept  at  rest 
at  the  same  temperature  and  away  from  the  neighbourhood 
of  moving  magnets  or  other  moving  currents,  we  obtain  this 
simple  uniform  current  in  all  parts  of  the  circuit. 

§  25.  It  will  be  obvious  that  this  simplicity  must  be 
widely  departed  from,  when  even  this  uniform  current  is  first 
started  and  when  it  ends,  and  that  simplicity  is  still  farther 
removed  from  the  case  in  which  currents  are  induced  by 
moving  magnets,  &c. ;  these  currents  must  vary  at  every 
moment  in  any  one  place,  and  differ  at  all  parts  of  the  circuit. 
To  take  the  simplest  case  first :  when  the  poles  of  the  galvanic 
cell  z  c  are  first  joined  at  n  and  m  to  the  wires  A  B  c  D 
electricity  will  rush  from  the  cell  into  the  wires ;  this  elec- 
tricity has  to  charge  each  portion  of 
the  wires  statically :  the  current  begins 
close  to  the  cell  some  time  before 
it  reaches  the  remoter  portions  of 
the  wire;  it  flows  at  different  rates 
through  different  sections  of  the  wire, 
according  to  their  size,  capacity,  and 
material ;  it  induces  currents  in  all  conductors  in  the  neigh- 
bourhood, and  is  checked  while  doing  so,  and  not  until  all 
this  is  over  shall  we  have  that  permanent  condition  in  which 
a  constant  current  flows  through  all  parts  of  the  circuit. 
The  series  of  phenomena  just  described  occurs  whenever 
an  electric  signal  is  sent  along  a  wire.  The  earth  generally 
forms  one  part  of  the  circuit  used  for  this  purpose,  and  the 
circuit  is  completed  or  closed  by  making  contact  at  one 
place  only,  as  at  m,  the  wire  at  n  being  already  joined  to  z ; 


CHAP.  III.]  Current.  79 

the  phenomena  are  not  made  at  all  simpler  by  these  changes. 
The  speed  of  electricity  is  often  spoken  of,  but  what  has 
now  been  said  shows  that  these  words  without  qualification 
can  have  no  meaning  ;  electricity  starting  from  m  does  not 
reach  A,  B  or  c  like  a  bullet,  but  in  a  gradually  increasing 
wave,  and  the  manner  and  rate  of  its  arrival  depend  evi- 
dently on  many  circumstances,  such  as  the  size  and  material 
of  the  wire,  its  distance  from 
surrounding  conductors,  &c. 


If  the  cell  be  connected  with  - 
two  long  wires  insulated  at 
the  further  ends  (as  in  Fig. 
51),  or  if  one  pole  be  connected  with  the  earth  and  the 
other  with  a  large  insulated  conductor  or  long  wire,  we 
shall  have  a  series  of  precisely  similar  phenomena,  except 
that  the  final  condition  of  equilibrium  will  be  that  in  which 
all  parts  of  the  conductors  being  duly  charged  to  the 
potentials  which  the  cell  produces,  no  further  current  will 
flow  at  all. 

The  laws  according  to  which  the  varying  induced  currents 
flow  in  different  parts  of  the  circuit  are  subject  to  the  still 
further  complication,  that  the  inducing  system  does  not 
produce  any  constant  difference  of  potential  such  as  is  pro- 
duced by  the  cell,  and  that  even  the  current  which  it  induces 
in  any  one  part  of  the  circuit  varies  as  the  magnet  or 
inducing  system  varies  in  its  position  relatively  to  the 
circuit. 

§  26.  When  two  dissimilar  metals  (Fig.  27)  are  joined  so 
as  to  form  a  conducting  circuit,  and  the  junction  c  is  at  a 
different  temperature  from  the  junction  D,  an  electric  current 
is  found  to  flow  through  the  circuit,  a  difference  of  poten- 
tial or  E.  M.  F.  occurring  at  both  junctions.  In  both  cases, 
taking  iron  and  copper  below  300°  C.  as  an  example,  we 
should  have  the  tendency  to  send  the  current  from  the  iron 
to  the  copper  across  the  junction,  but  that  tendency  is 
greatest  at  the  cold  junction,  and  therefore  the  current  flows 


8o  Electricity  and  Magnetism.         [CHAP.  in. 

from  the  iron  to  the  copper  across  the  cold  junction.  The 
source  of  energy  here  is  heat,  which  is  absorbed  at  the  hot 
junction,  and  given  out  at  the  cold  junction ;  but  less  heat 
is  given  out  at  the  cold  than  is  absorbed  at  the  hot  junction 
by  an  amount  equivalent  to  the  work  done  by  the  electric 
current.  This  current  is  often  called  a  thermo-electric  cur- 
rent, but  it  differs  in  no  quality  from  other  currents.  The 
E.  M.  F.  produced  is  small. 

§  27.  In  conclusion,  we  have  found  that  currents  are 
produced  by  the  friction  of  non-conductors,  by  chemical 
reactions,  by  heat ;  by  the  approach,  commencement,  or 
increase  of  a  current  in  any  neighbouring  conductor  ;  by  the 
removal,  cessation,  or  diminution  of  any  neighbouring  cur- 
rent ;  by  the  motion  of  a  neighbouring  magnet  relatively 
to  a  conductor  and  by  the  increase  or  decrease  in  the 
magnetism  of  this  magnet. 

Lastly,  any  change  in  the  distribution  of  the  statical 
charge  of  electricity  on  the  surface  of  bodies  produces 
currents  until  the  redistribution  is  completed  and  equili- 
brium is  restored.  We  find  no  difference  of  kind  between 
all  these  currents ;  they  all  have  the  same  properties,  but 
combined  in  very  varying  degrees.  In  studying  the  laws 
which  connect  currents  with  other  electrical  magnitudes, 
we  find  that  we  must  distinguish  the  case  of  the  constant 
current  which  is  uniform  in  all  parts  of  the  circuit,  and  at 
rest  relatively  to  all  other  conductors  and  magnets,  from  that 
of  the  more  complex  varying  currents,  and  of  those  which 
move  relatively  to  other  currents,  conductors,  or  magnets. 


CHAP.  IV  Resistance.  8 1 

CHAPTER  IV. 

RESISTANCE. 

§  1.  BODIES  have  already  been  described  as  being  bad  or 
good  conductors,  and  an  imperfect  conductor  may  be  said 
to  oppose  the  passage  of  an  electric  current.  All  known 
conductors  oppose  a  sensible  resistance  to  the  passage  of  a 
current,  by  which  we  mean  that  if  two  bodies  of  any  sensible 
capacity  and  at  different  potentials  be  joined,  the  current 
produced  occupies  a  sensible  time  in  passing  between  them, 
whatever  material  be  employed  to  join  the  bodies,  and  how- 
ever it  may  be  shaped.1  The  strength  of  the  current,  or,  in 
other  words,  the  quantity  of  electricity  passing  per  second 
from  one  point  to  another,  when  a  constant  difference  of 
potentials  is  maintained  between  them,  depends  on  the  re- 
sistance of  the  wire  or  conductor  joining  those  two  points. 
A  bad  conductor  does  not  let  the  electricity  pass  so  rapidly 
as  a  good  conductor,  or,  in  other  words,  a  bad  conductor 
offers  more  resistance  than  a  good  one.  When  no  electro- 
magnetic phenomena  are  produced,  the  current  flowing 
from  a  point  at  potential  A  to  a  point  at  potential  B  depends 
simply  on  what  is  here  called  the  resistance  of  the  conductor 
separating  them. 

§  2.  With  a  given  conductor  joining  two  points,  it  is  found 
by  experiment  that  upon  doubling  the  difference  of  potential 
between  the  points,  twice  as  strong  a  current  flows  as 
before  ;  in  other  words,  with  a  constant  resistance,  the 
current  is  simply  proportional  to  the  E.  M  .  F.  or  difference  of 
potentials  between  the  points.  Again,  it  is  found  that  keep- 
ing the  difference  of  potential  constant,  and  keeping  the 
section  and  material  of  the  conducting  wire  constant  but 
doubling  its  length,  we  halve  the  current  which  flows,  and 

1  The  self-induction  of  a  current  would  cause  a  delay  in  its  passage 
between  two  points  even  if  the  conductor  had  no  resistance,  but  the 
delay  due  to  resistance  is  easily  separated  from  that  due  to  self-induction. 

G 


82  Electricity  and  Magnetism.         [CHAP.  IV. 

generally  that  if  the  E.  M.  F.  and  section  and  material  of  the 
wire  be  kept  constant,  the  current  will  be  inversely  pro- 
portional to  the  length  of  the  conductor.  Again,  keeping 
the  E.  M.  F.,  length,  and  material  all  constant  the  current  is 
halved  by  halving  the  area  of  the  cross  section  of  the  wire. 
Consequently,  if  we  define  resistance  as  proportional  to  the 
length  of  the  wire  of  constant  section,  and  as  inversely  pro- 
portional to  the  cross  section  where  that  varies,  we  shall  be 
justified  in  saying  that  with  a  given  difference  of  potentials 
or  E.  M.  F.  between  two  points,  the  current  which  flows  will 
be  inversely  proportional  to  the  resistance  separating  these 
points  ;  and,  again,  that  with  a  constant  resistance  separating 
two  points,  the  current  flowing  will  be  simply  proportional 
to  the  E.  M.  F.  or  difference  of  potential  between  the  points. 
If,  then,  we  call  c  the  current,  I  the  electromotive  force, 
and  R  the  resistance  of  the  conductor,  we  find  that  c  is 

proportional  to  the  quotient  — ,  and  is  affected  by  no  other 

R 

circumstance,  hence  we  have 

c  =    — ,  or  R  —  -,  or  i  =  c  R. 

This  equation  expresses  Ohm's  law,  which  may  be  stated 
thus  : — 

When  a  current  is  produced  in  a  conductor  by  an  E.  M.  F.  the 
ratio  of  the  E.  M.  F.  to  the  current  is  independent  of  the  strength 
of  the  current,  and  is  called  the  resistance  of  the  conductor. 

This  definition  of  resistance  would  not  be  justified  if 
we  did  not  always  obtain  one  and  the  same  value  for  R 
in  any  one  conductor,  whatever  electromotive  force  may  be 
employed  to  force  a  current  through  it.  The  electrical 
resistance  of  a  conductor  is  not  analogous  to  mechanical 
resistance,  such  as  the  friction  which  water  experiences  in 
passing  through  a  pipe,  for  this  frictional  resistance  is  not 
constant  when  different  quantities  of  water  are  being  forced 
through  the  pipe,  whereas  the  magnitude  called  electrical 
resistance  is  quite  constant  whatever  quantity  of  electricity 
be  forced  through  the  conductor.  This  fact  leads  to  much 


CHAP.  IV.]  Resistance.  83 

greater  simplicity  in  the  calculations  of  the  distribution  of 
electrical  currents  than  in  calculations  of  the  flow  of  water. 
The  accuracy  of  Ohm's  law  is  most  easily  illustrated  with 
a  galvanometer  having  a  short  coil  of  thick  wire.  Take  a 
Grove's  cell  and  make  a  circuit  through  the  galvanometer, 
and  such  a  length  of  fine  wire  as  gives  a  convenient  deflec- 
tion, it  will  be  found  that  the  deflection  is  nearly  inversely 
proportional  to  the  length  of  the  fine  wire  ;  when  this  length 
is  doubled,  the  deflection  is  halved.  This  would  be  strictly 
true  if  the  deflections  of  the  galvanometer  were  proportional 
to  the  current,  and  if  the  resistance  of  the  galvanometer  and 
of  the  cell  were  nil  Taking  these  resistances  into  account, 
then,  with  any  cell  or  battery  of  constant  E.  M.  F.  and  with 
any  galvanometer,  we  shall  find  the  deflections  inversely 
proportional  to  the  total  resistances  of  the  circuit. 

§  3.  Resistance  in  a  wire  of  constant  section  and  material 
is  directly  proportional  to  the  length  and  inversely  proportional 
to  the  area  of  the  cross  section.  The  form  of  the  cross  section 
is  a  matter  of  indifference,  showing  that  the  resistance  is 
in  no  way  affected  by  the  extent  of  surface  of  the  conducting 
wire  or  rod,  and  that  although  electricity  at  rest  is  found  only 
on  the  surface,  electricity  when  flowing  as  a  current  is  pro- 
pagated along  all  parts  of  the  conductor  alike. 

The  most  easily  explained  manner  of  comparing  two  resist- 
ances is  by  means  of  the  differential  galvanometer.  Let  the 
coil  of  a  galvanometer  be  formed  of  two  insulated  wires  wound 
on  side  by  side,  so  that  each  makes  the  same  number  of  turns. 
Then  if  equal  currents  be  sent  round  the  two  coils  in  oppo- 
site directions  there  will  be  no  deflection;  if  the  two  currents 
be  not  equal,  the  stronger  will  produce  a  deflection.  Let 
GJ  G  represent  the  two  coils  in  the  annexed  diagram,  and 
let  RJ  R  be  two  resistances  which  are  to  be  compared  ;  join 
the  two  galvanometer  coils  at  B  and  the  two  resistances  at  A 
connecting  RJ  with  G}  and  R  with  G,  as  shown;  complete 
the  circuit  by  connecting  B  with  A,  through  a  battery  c  z. 
One  portion  of  the  current  will  pass  through  G  R,  the  other 

G2 


84 


Electricity  and  Magnetism.         [CHAP.  IV. 


FIG,  52. 


portion  through  G}  RJ.  The  magnitude  of  the  current  through 
both  these  conductors  depends  on  their  resistance  and  on  the 
difference  of  potential  between  A  and 
B  which  is  the  same  in  both  cases. 
Hence  the  current  through  G  and  R  will 
be  equal  to  the  current  through  Gt  and 
R!  if  the  resistances  of  the  two  branches 
are  equal.  It  is  easy  to  make  the  resist- 
ance of  Gj  equal  to  the  resistance  of  G, 
by  adding  a  little  piece  of  wire  to  the 
coil  which  has  the  smallest  resistance  if 
there  be  any  difference  between  them. 
If  therefore  we  find  no  deflection 
caused  by  completing  the  circuit  as 
above  we  may  conclude  that  R  =  i^. 
If  R!  be  the  greater,  less  current  will 
pass  through  GJ  than  through  G  and  a 
deflection  in  one  direction  will  follow  ; 
a  deflection  in  the  opposite  direction 
would  be  produced  if  R,  were  the  smaller.  It  is  easy  by  suc- 
cessive trials  to  find  the  relative  lengths  of  two  wires  R  and  RJ 
which  balance  one  another  when  different  materials  or  differ- 
ent forms  are  used.  By  this  instrument  the  law  stated  at  the 
beginning  of  the  paragraph  is  easily  proved. 

§  4.  Since  the  resistance  of  a  wire  of  any  given  material  is 
inversely  proportional  to  the  cross  section  of  the  wire,  it 
will  also  be  inversely  proportional  to  the  weight  per 
unit  of  length  ;  or,  in  other  words,  the  resistance  of  a  uniform 
wire  of  any  material  is  Inversely  proportional  to  the  weight 
per  foot  of  the  wire,  i.e.  a  wire  weighing  twenty  grains  per 
foot  has  half  the  resistance  of  a  wire  weighing  ten  grains  per 
foot.  Inasmuch  as  all  bodies  have  not  the  same  specific 
gravity,  the  relative  resistance  of  different  materials  will 
be  different,  according  as  we  refer  them  to  similar  cross 
sections  and  lengths,  or  to  similar  weights  and  lengths. 
When  treating  of  the  measurement  of  resistance,  a  Table 


CHAP.  IV.]  Resistance.  85 

will  be  given  in  which  the  relative  resistances  of  various 
materials  are  given,  referred  to  both  units ;  meanwhile,  it 
may  be  sufficient  to  state  that  pure  copper  or  pure  silver 
have  smaller  resistances  than  any  other  known  material; 
that  alloys  have  a  larger  resistance  than  metals  ;  electro- 
lytes a  considerably  greater  resistance  than  most  alloys ; 
that  some  liquids,  such  as  oil,  have  so  great  a  resistance 
as  to  become  insulators,  but  that  all  known  insulators, 
except  gases,  do  permit  the  passage  of  electricity  in  a  way 
differing  rather  in  degree  than  in  kind  from  the  way  in 
which  metals  permit  the  passage  of  electricity.  Thus  bad 
conductors  or  insulators  will  hereafter  be  frequently  spoken 
of  as  bodies  of  great  resistance.  The  difference  in  this 
respect  between  an  insulator  and  a  good  conductor  is  enor- 
mous. Taking  the  resistance  of  silver  at  o°  C.  as  the  unit, 
a  wire  of  equal  length  and  diameter  of  German  silver  would 
have  a  resistance  of  12-82,  and  a  rod  of  gutta  percha  of  equal 
bulk  and  length  about  850,000,000,000,000,000,000,  or 
8'5  x  io20;  nevertheless,  Ohm's  law  applies  to  the  resist- 
ance of  each  material. 

§  5,  The  resistance  of  all  materials  alters  with  a  change  of 
temperature.  With  the  metals  and  good  conductors,  the 
resistance  becomes  greater  with  a  rise  of  temperature  ;  with 
electrolytes  and  bad  conductors  it  diminishes.  There  is  thus 
less  difference  between  the  resistances  of  these  dissimilar 
bodies  at  high  temperatures  than  at  low.  Inasmuch  as  the 
passage  of  a  current  through  a  wire  heats  it,  the  passage  of  a 
current  tends  continually  to  increase  the  resistance  which  it 
meets  with.  This  can  easily  be  seen  with  a  differential  gal- 
vanometer. After  carefully  balancing  R  and  Rb  Fig.  52,  alter 
the  circuit  so  as  to  pass  the  current  for  some  minutes  through 
R!  andGj  only.  On  reconnecting  R  and  G  a  deflection  will  be 
observed,  and  R  will  have  to  be  increased  to  balance  RI? 
until  the  wires  have  been  left  to  resume  their  former  tempera- 
ture. Wires  of  graduated  length  and  section,  insulated  by 
silk  and  wound  on  bobbins  are  employed  to  represent  certain 


86  Electricity  and  Magnetism.         [CHAP.  IV. 

definite  resistances,  and  these  bobbins  of  insulated  wire  are 
called  resistance  coils.  It  is  essential  inat  they  should  be 
made  of  a  material,  such  as  German  silver,  the  resistance  of 
which  varies  little  with  a  change  of  temperature,  and  that  in 
careful  experiments  the  temperature  of  the  resistance  coil 
should  be  noted  and  allowed  for. 

§  6,  A  knowledge  of  the  resistance  of  a  conductor  is 
essential  to  determine  how  much  electricity  will  flow  between 
two  points  in  a  given  time  when  joined  by  that  conductor; 
in  other  words,  to  determine  the  strength  of  a  current  which 
will  under  any  given  circumstances  be  produced;  how 
much  the  current  will  be  modified  by  a  change  in  any  given 
conductor;  how  a  current  will  be  subdivided  and  affected  by 
having  two  or  more  paths  open  to  it  between  the  same 
points  ;  to  determine  the  effect  of  galvanic  cells  of  different 
sizes  and  materials,  since  each  kind  of  galvanic  cell  has  an 
internal  resistance  depending  on  the  size  of  the  plates,  on 
the  distance  between  them,  and  on  the  solutions  employed ; 
to  allow  a  comparison  between  the  qualities  of  insulators ; 
and  to  enable  us  to  augment,  diminish,  and  in  all  ways  regu- 
late any  current  at  will. 

§  7.  The  resistance  of  the  materials  of  which  any  gal- 
vanic cell  is  made  limits  the  current  which  it  can  produce. 
When  the  two  metals  are  joined  by  the  shortest  and  thickest 
wire  practicable,  the  resistance  of  the  circuit  is  practically 
the  internal  resistance  of  the  battery,  and  in  most  forms  this 
is  very  considerable.  In  a  sawdust  Daniell  it  is  often  more 
than  the  resistance  of  a  mile  of  No.  8  iron  wire,  the  size 
usually  employed  for  land  lines  of  telegraph  :  a  quarter  of 
a  mile  of  such  wire  is  a  small  resistance  for  a  DanielFs  cell. 
The  resistance  of  the  Grove  cell  is  much  smaller.  The 
resistance  of  a  battery  decreases  as  the  size  of  the  plates  is 
increased,  because  this  is  equivalent  to  increasing  the  area 
of  the  cross  section  of  the  liquids,  the  resistance  of  which  is 
from  i  to  20  million  times  as  great  as  that  of  metals  of  the 
same  size. 


CHAP.  IV.] 


Resistance. 


Take  two  cells  of  any  battery,  join  them  as  in  Fig.  53, 
the  copper  being  connected  to  the  copper  and  the  zinc  to 
the  zinc.  Cells  thus  joined  are  said  to  be  joined  in  multiple 
arc.  The  two  cells  are  exactly  equivalent  to  a  single  cell  of 
double  the  size.  The  E.  M.  F.  produced  is  that  of  one  cell ; 
the  resistance  is  half  that  of  one  cell.  Complete  a  circuit  by 
inserting  a  galvanometer  with  a  short  thick  coil  between  c 
and  z ;  the  deflection  obtained  will  be  nearly  double  that 
which  the  one  cell  gives  through  the  same  galvanometer, 
because  halving  the  resistance  of  the  cell  very  nearly  halves 
the  resistance  of  the  whole  circuit.  Next,  make  a  circuit 


FIG.  53. 


FIG.  54. 


with  one  of  the  two  cells  and  a  galvanometer  with  a  com- 
paratively long  coil  of  fine  wire,  reducing  the  current  so  as 
to  have  a  convenient  deflection  by  adding  a  resistance  R  if 
necessary.  Add  the  second  cell  in  multiple  arc ;  no  visible 
change  will  be  produced  in  the  deflection,  because  the  resist- 
ance of  the  circuit  is  now  chiefly  made  up  of  that  of  the  gal- 
vanometer and  resistance  R.  Diminishing  the  resistance  of 
the  battery  hardly  alters  the  whole  resistance  and  does  not 
sensibly  alter  the  current.  Thirdly,  join  the  two  cells  in  the 
manner  described  in  Chapter  I.  §  19,  the  zinc  being  joined  to 
the  copper  as  in  Fig.  13  or  Fig.  54.  This  manner  of  joining  is 
described  by  the  words  ;  in  series.'  Now  complete  the  circuit 
with  the  fine  wire  galvanometer  and  R,  as  in  the  second  expeii- 


88  Electricity  and  Magnetism.         [CHAP.  IV. 

ment.  The  deflection  will  be  nearly  doubled.  The  resistance 
has  been  slightly  increased  by  adding  the  second  cell  in  series, 
but  the  resistance  of  the  batteries  is  only  an  insignificant  por- 
tion of  the  whole  ;  while  therefore  the  resistance  of  the  circuit 
has  hardly  been  changed,  the  E.  M.  F.  has  been  doubled  by 
doubling  the  number  of  metallic  junctions,  and  twice  the 
E.  M.  F.  with  a  constant  resistance  gives  twice  the  current  and 
twice  the  deflection.  Fourthly,  return  to  the  thick  wire  gal- 
vanometer, complete  the  circuit  through  it  with  the  two  cells 
in  series ;  the  deflection  will  be  almost  exactly  the  same  as 
when  one  cell  only  is  used,  and  only  half  that  obtained  when 
the  two  cells  are  joined  in  multiple  arc.  When  the  two  cells 
were  joined  in  series  the  E.  M.  F.  was  doubled,  but  the  resist- 
ance of  the  whole  circuit  was  also  nearly  doubled  and  there- 
fore the  current  remained  nearly  the  same  as  before.  Thus 
we  see  that  with  a  short  circuit  of  small  external  resistance 
we  can  increase  the  current  by  increasing  the  size  of  cells,  or, 
what  is  equivalent  to  this,  by  joining  several  cells  in  multiple 
arc.  We  can  also  increase  the  current  by  employing  liquids 
of  smaller  specific  resistance,  but  we  cannot  increase  the 
current  by  adding  cells  in  series.  With  a  long  circuit  of 
great  external  resistance  large  cells,  or  many  of  them  joined 
in  multiple  arc,  will  fail  to  give  us  strong  currents,  but  we 
may  increase  the  current  by  joining  the  same  cells  in  series. 

When  the  resistance  of  the  battery  is  neither  excessively 
large  nor  excessively  small  in  comparison  with  that  of  the 
rest  of  the  circuit  the  current  will  be  increased  both  by 
adding  cells  in  series  and  by  increasing  their  size  or  adding 
them  in  multiple  arc.  By  the  former  process  we  increase 
the  E.  M.  F.  more  than  we  increase  the  resistance.  By  the 
latter  process  we  sensibly  diminish  the  resistance  of  the 
circuit,  leaving  the  E.  M.  F.  unaltered. 

Cells  joined  in  series  are  sometimes  described  as  joined 
for  intensity,  and  cells  joined  in  multiple  arc  as  joined  for 
quantity.  These  terms  are  remnants  of  an  erroneous 
theory. 


CHAP.  IV.]  Resistance.  89 

§  8.  The  resistance  of  the  galvanometer  employed  to 
indicate  a  current  in  a  circuit  is  a  very  material  element  in 
the  circuit.  A  powerful  current  may  be  flowing  from  a 
large  cell  through  a  circuit  of  small  resistance.  If  we  intro- 
duce a  galvanometer  having  a  long  coil  of  thin  wire,  we 
may  by  that  very  act  diminish  the  current  a  thousand-fold. 
For  circuits  of  small  resistance  galvanometers  of  small  re- 
sistance must  be  used.  For  circuits  of  large  resistance 
galvanometers  of  large  resistance  must  also  be  used ;  not 
that  their  resistance  is  any  advantage,  but  because  we 
cannot  have  a  galvanometer  adapted  to  indicate  very  small 
currents  without  having  a  very  large  number  of  turns  in  the 
coil,  and  this  involves  necessarily  a  large  resistance. 

§  9.  There  are  several  forms  of  apparent  resistance  which 
are  not  resistances. 

When  a  current  passes  to  or  from  a  metal  to  a  liquid 
electrolyte,  a  great  apparent  resistance  occurs,  i.e.  the 
current  is  diminished  by  the  change  of  medium  much  more 
than  by  a  considerable  length  of  either  material.  This 
resistance  is  sometimes  said  to  be  due  to  the  polarisation 
of  the  metals  dipped  into  the  solution.  This  word  polarisa- 
tion is  sometimes  very  vaguely  employed,  but  apparently  here 
it  means  that  the  plates  become  coated  with  the  products  of 
the  decomposition  of  the  electrolyte,  and  that  this  coating 
produces  a  diminution  of  current.  This  diminution,  which  of 
course  affects  the  current  throughout  its  entire  length,  does 
not,  however,  appear  to  be  due  to  anything  analogous  to 
resistance.  The  effect  in  question  is  due  to  something  in 
the  nature  of  a  reciprocating  force  by  which  energy  is 
stored  up,  i.e.  when  the  original  current  ceases,  a  current  in 
the  opposite  direction  is  set  up  at  these  surfaces  of  passage 
from  liquid  to  solid  by  a  kind  of  rebound.  It  appears,  there- 
fore, that  the  current  has  been  diminished  by  the  creation  of 
an  opposing  electromotive  force  due  to  the  arrangement  of 
the  elements  into  which  the  electrolyte  itself  has  been 
decomposed.  The  term  resistance  is,  however,  continually 


9°  Electricity  and  Magnetism.         [CHAP.  IV. 

applied  to  this  cause  of  the  diminution  of  a  current  even  by 
those  who  are  convinced  that  the  diminution  is  not  due  to  a 
true  resistance.  This  false  resistance  or  polarisation  is  easily 
observed.  Make  a  circuit  of  a  galvanometer,  a  copper  wire, 
two  Daniell's  cells,  and  a  couple  of  plates  of  one  metal  sepa- 
rated by  water  or  any  electrolyte.  The  deflection  of  the 
galvanometer  during  the  first  few  minutes  will  be  found  to 
decrease  rapidly  ;  then  if  the  cell  be  removed  and  the  circuit 
closed,  the  two  metal  plates  will  send  a  current  deflecting 
the  galvanometer  in  the  opposite  direction  ;  this  current  is 
strongest  at  first,  and  gradually  ceases  altogether. 

§  10.  When  a  current  begins  to  flow  across  a  solid  in- 
sulator, such  as  gutta  percha,  a  very  similar  phenomenon 
occurs  ;  the  current  gradually  and  rapidly  diminishes,  as  if 
the  resistance  of  the  gutta  percha  increased  under  the 
influence  of  the  current.  This  apparent  extra  resistance 
is,  however,  no  true  resistance  ;  when  the  original  current 
ceases,  the  gutta  percha  sends  back  a  gradually  decreasing 
current  in  the  opposite  direction,  and  this  current  is  of 
such  magnitude  and  lasts  for  such  a  time  as  precisely  to 
send  back  all  the  electricity  which  had,  at  first,  apparently 
flowed  through  the  gutta  percha  in  excess  of  the  quantity 
which  would  have  passed  in  the  same  time  through  a  con- 
stant resistance  equal  to  the  final  resistance.  The  final 
resistance  of  the  gutta  percha  is  looked  upon. by  some  elec- 
tricians as  its  true  resistance,  inasmuch  as  it  is  the  only  part 
of  the  apparent  resistance  which  follows  Ohm's  law ;  the 
greater  flow  of  current  in  the  first  instance  is,  according  to 
this  view,  due  not  to  a  diminished  resistance,  but  to  an  appa- 
rent absorption  of  electricity,  as  if  by  a  number  of  condensers. 
Other  electricians  look  upon  this  property  of  the  solid 
insulator  or  electrolyte  as  quite  analogous  to  the  polarising 
property  of  the  liquid  electrolyte,  and  consider  that  the 
resistance  of  the  material,  as  shown  by  the  first  current,  is  the 
true  resistance  and  the  subsequent  diminution  of  current  is 


CHAP.  IV.] 


Resistance. 


FIG.  55. 


due  to  an  opposing  electromotive  force.     The  former  view 
appears  to  the  writer  to  be  the  more  tenable. 

This  phenomenon  is  most  easily  observed  with  the  aid  of 
a  considerable  length  of  wire  insulated  with  india-rubber  or 
gutta  percha.  Take,  say,  a  mile  of  such  insulated  copper  wire 
as  is  used  for  submarine  telegraph  cables  ;  place  it  in  a  tub  of 
water ;  insulate  one  end  n  of  the  wire  and  connect  the  other 
m  through  a  galvanometer  G  with  one  pole  of  a  galvanic 
battery  c  z  of  say  50 
cells.  Connect  the 
other  pole  of  the 
battery  with  the  wa-  c 
ter  by  a  copper  plate, 
as  in  Fig.  55.  The 
galvanometer  must 
have  a  coil  with  some  thousands  of  turns  of  fine  wire. 
All  the  connections  must  be  carefully  insulated.  When 
all  the  other  arrangements  have  been  completed  the  cir- 
cuit may  be  completed  by  joining  the  wires  at  m  ;  this 
will  be  followed  by  a  violent  throw  of  the  galvanometer 
needle,  due  to  the  rapid  rush  of  the  electricity  to  charge  the 
wire.  When  the  needle  comes  to  rest  a  steady  deflection  in 
the  same  direction  will  be  observed,  due  to  a  current  flowing 
from  c  through  G  and  across  the  gutta  percha  sheath  to  the 
water  and  thus  to  z.  This  deflection  will  gradually  diminish, 
until  after  an  hour  it  may  be  two-thirds  or  half  the  original 
deflection.  Call  this  final  deflection  x  and  the  deflections 
at  each  minute  after  the  wires  at  m  were  joined 


Now  remove  the  cell  c  z  and  substitute  for  it  a  metallic  con- 
nection, as  shown  by  the  dotted  line.  This  may  be  done  by 
means  of  prearranged  stops  or  keys  so  as  not  to  disturb  the 
insulation  of  any  part.  Then  the  charge  in  the  wire  "will 
rush  out  through  G,  causing  a  violent  throw  in  the  opposite 


92  Electricity  and  Magnetism.         [CHAP.  IV. 

direction  to  that  produced  by  the  charge  and  equal  in  amount. 
After  this  discharge  has  taken  place  a  steady  deflection  will 
be  observed  in  the  same  direction  as  that  due  to  the  discharge, 
and  this  deflection  at  the  end  of  each  successive  minute  will 
be  equal  to  0X  a2  az  .  .  .  aGQ.  It  is  assumed  that  a  reflect- 
ing galvanometer  is  used,  in  which  the  deflections  are  pro- 
portional to  the  currents.  The  violence  of  the  charge  and 
discharge  is  such  that  in  delicate  experiments  they  are  not 
allowed  to  flow  through  the  galvanometer,  but  are  conducted 
across  between  the  terminals  by  what  is  termed  a  short 
circuit,  being  a  connection  of  small  resistance  temporarily 
inserted. 

§  11.  Electricity  is  not  only  conducted  from  one  body  to 
another,  by  flowing  as  a  current  along  a  conductor  ;  it  may 
also  be  conveyed  or  carried  in  a  solid  conductor,  through 
such  an  insulator  as  air,  from  one  place  to  another.  When 
two  conductors  charged  to  very  different  potentials  are 
brought  close  together,  the  attraction  of  the  electricity  is 
such  that  it  tears  off  the  metal  or  material  in  fine  powder, 
and  this  powder  springs  across  the  intervening  space, 
carrying  with  it  a  charge  of  electricity.  The  air  or  gas 
itself  is  also  electrified  by  contact  with  the  conductor, 
and  helps  to  convey  the  electricity.  Light  and  heat  are 
evolved  in  the  process  apparently  much  as  light  and  heat 
are  evolved  when  sparks  are  struck  from  steel.  Electric 
sparks  thus  produced  are  said  to  overcome  the  resistance  of 
the  air,  but  this  resistance  has  nothing  in  common  with  the 
resistance  which  is  the  subject  of  Ohm's  law.  The  laws 
according  to  which  sparks  pass,  and  brushes,  as  they  are 
called,  form  on  points  electrically  charged,  must  be  sepa- 
rately studied.  The  brush  discharges,  whether  luminous  or 
otherwise,  are  due  to  the  accumulation  of  electricity  in 
large  quantities  at  points.  The  electricity  has  such  a  re- 
pulsion for  itself,  that  if  it  accumulates  sufficiently,  the  force 
becomes  great  enough  to  break  down  the  pressure  of  the 
air,  and  highly  electrified  particles  of  the  conductor  and  of 


CHAP,  iv.]  Resistance.  93 

air  fly  off  the  point.  Every  electrical  spark  seen  is  an  illus- 
tration of  this  convection.  Lightning  is  one  example; 
another  is  the  luminous  brush  which  in  the  dark  may  be 
observed  discharging  the  conductors  of  an  electrical  fric- 
tional  machine.  The  air  or  gas  heated  by  the  spark  pro- 
bably conducts  some  electricity,  so  that  only  part  of  the 
electricity  passing  in  the  spark  or  brush  is  transferred  by 
convection. 

§  12.  Rarefied  gases  are  found  to  be  tolerably  good 
conductors.  The  laws  of  their  resistance  to  the  passage  of 
electricity  have  only  lately  been  investigated,  and  are  but 
partially  understood.  It  is  uncertain  how  far  their  resistance 
can  properly  be  said  to  follow  Ohm's  law.  According  to 
recent  experiments  by  Mr.  Varley,  conduction  in  rarefied 
gases  does  follow  Ohm's  law,  but  there  is  a  very  large 
resistance  at  the  surface  of  contact  between  the  attenuated 
gas  and  the  metal  conductor.  This  resistance  is  con- 
stant and  prevents  any  current  from  passing  until  the  E.  M.  F. 
employed  exceeds  a  certain  definite  magnitude,  which  is  con- 
stant for  each  material  and  degree  of  rarefaction.  This  is 
very  analogous  to  what  takes  place  in  eleetrolytes,  except  thai 
through  these  some  current  apparently  always  passes  whatever 
E.  M.  F.  be  employed,  although  no  complete  decomposition  oc-' 
curs  until  a  certain  definite  E.  M.  F.,  constant  for  each  electro- 
lyte, has  been  reached.  Experiments  showing  the  action  of  a 
partial  vacuum  can  be  made  with  Geissler's  tubes,  which  can 
be  bought  at  any  respectable  optician's.  These  glass  tubes 
contain  highly  rarefied  gases,  and  electrodes  leading  through 
the  glass  are  employed  as  part  of  the  circuit.  If  a  galvano- 
meter and  an  electric  battery  form  part  of  the  circuit  no 
current  will  be  observed  until  perhaps  two  hundred  cells  are 
employed.  Then  the  current  passes  with  brilliant  optical 
effects  in  the  tube  and  the  galvanometer  is  deflected.  Induc- 
tion apparatus  producing  high  electromotive  force,  such  as 
the  well-known  RuhmkorfFs  coil,  may  be  employed  instead 
of  the  galvanic  battery. 


94  Electricity  and  Magnetism.  [CHAP.  V. 

CHAPTER  V. 

ELECTRO-STATIC   MEASUREMENT. 

§  1.  OUR  knowledge  of  electricity  and  magnetism  is  derived 
from  observation  of  certain"  forces,  and  the  comparison  of 
currents,  quantities,  potentials,  and  resistances  are  all  effected 
by  a  comparison  of  forces  acting  under  various  circum- 
stances. The  measurement  of  forces  requires  fixed  stand- 
ards of  length,  mass,  and  time,  which  will  also  serve  as 
fundamental  standards  for  all  electrical  measurements.  The 
centimetre  .  .  .  gramme  .  .  .  second 

are  the  three  units  of  length,  mass,  and  time  which  will  be 
adopted  in  the  present  treatise. 

As  stated  in  Chapter  I.  §  17,  the  unit  of  Force  adopted 
by  us  is  the  force  which  will  produce  a  velocity  of  one  centi- 
metre per  second  in  a  free  mass  of  one  gramme  by  acting 
on  it  for  one  second. 

This  unit  of  force  =  '00101915  x  weight  of  a  gramme 
at  Paris.  The  weight  of  the  gramme  itself  wherever  we 
•  happen  to  be  is  the  more  common  unit  of  force,  but  we  shall 
find  the  so-called  absolute  unit  more  convenient  in  calcula- 
tions, and  any  result  can  be  readily  reconverted  into  the 
more  familiar  measure  by  multiplying  it  into  the  above 
coefficient,  or  dividing  it  by  the  number  980-868. 

The  unit  of  work  is  the  work  performed  by  the  unit  force 
moving  over  a  distance  of  one  centimetre ;  it  is  equal  to 
•00101915  centimetre  grammes;  in  other  words,  to  lift 
the  weight  of  one  gramme  through  one  centimetre  at  Paris 
requires  an  expenditure  of  work  equal  to  980-868  of  the  units 
of  work. 

§  2.  In  what  is  termed  electro-static  measure  the  unit 
quantity  of  electricity  is  that  which  exerts  the  unit  force  on 
a  quantity  equal  to  itself  at  a  distance  of  one  centimetre 
across  air. 


CHAP.  V.]  Electro-static  Measurement.  95 

The  unit  difference  of  potential  or  unit  electromotive 
force  exists  between  two  points  when  the  unit  of  work  is 
spent  by  a  unit  of  electricity  in  moving  from  one  to  the 
other  against  the  electric  repulsion,  described  in  Chapter  I. 

The  resistance  of  a  conductor  between  two  points  is  a 
unit  if  it  allows  only  one  unit  of  electricity  per  second  to 
pass  from  one  to  the  other  when  the  unit  of  electromotive 
force  is  maintained  between  them. 

The  system  of  electrical  units  as  denned  in  this  paragraph 
is  called  the  electro-static  absolute  system,  based  on  the  cen- 
timetre, gramme,  and  second.  No  special  names  have  yet 
been  given  to  these  units.  They  are  the  most  convenient  for 
use  when  dealing  with  the  phenomena  described  in  Chapter  I. 
The  equations  expressing  these  definitions  are  given  below 
in  §  14. 

§  3.  It  is  found  by  experiment  that  the  force  f  with 
which,  at  a  given  distance  d,  two  small  electrified  bodies 
repel  or  attract  one  another,  is  proportional  to  the  product 
of  the  charges,  q  and  q^  upon  them  ;  and  further,  that  when 
the  distance  varies  this  force  f  is  inversely  proportional  to 
the  square  of  the  distance  d  between  them;  it  follows,  from 
the  definition  adopted  of  force  and  quantity,  that 

/=   ^'  d) 

from  which  equation,  if  we  observe  the  force,  and  make  q 
either  equal  to  q^  or  to  bear  any  known  relation  to  it,  we  can 
determine  the  quantity  q  in  absolute  measure ;  or  vice  versa, 
knowing  q  and  q^  we  can  determine  what  force  they  will 
exert  at  a  given  distance,  as,  for  instance,  in  moving  the 
index  of  an  electrometer.  The  application  of  this  equa- 
tion is  limited  to  small  electrified  bodies.  In  any  body  of 
sensible  size  the  mutual  induction  between  the  two  electri- 
fied bodies  would  disturb  the  distribution  of  electricity  over 
the  surface,  and  change  that  distribution  at  every  distance. 

§  4.  The  quantity  of  electricity  with  which  a  given  con- 
ductor in  a  given  place  can  be  charged  depends  simply  on 
the  difference  of  potential  between  it  and  neighbouring  con- 


g6  Electricity  and  Magnetism.          [CHAP.  V. 

ductors,  and  if  these  neighbouring  conductors  are  uninsu- 
lated we  may  say  that  the  charge  will  be  simply  proportional 
to  the  potential  of  the  body  charged  ;  we  may  therefore 
speak  of  the  capacity  s  of  a  given  conductor  for  electricity, 
meaning  thereby  the  constant  quotient  of*  the  quantity  on 
the  conductor  divided  by  its  potential;  or  calling  the  quantity 
q,  as  before,  and  the  potential  /,  we  have 

q  —  si  (2) 

The  capacity  of  a  sphere  at  a  distance  from  all  conductors 
is  equal  to  its  radius;  that  is  to  say,  a  sphere  one  metre  in 
diameter  will,  when  charged  to  the  potential  6,  contain 
6  x  50,  or  300  units  of  electricity. 

The  capacity  jy  of  a  sphere  of  radius  x,  suspended  in  the 
centre  of  a  hollow  uninsulated  sphere,  radius  7,  is 


The  dielectric  separating  the  two  spheres  is  supposed  to  be 
air.  The  capacity  of  the  internal  conductor  would  change 
if  any  other  dielectric  were  used.  The  capacity  of  a  metal 
conductor  is  independent  of  the  metal  employed.  The 
phenomenon  is  more  complex  when  either  solid  or  liquid 
electrolytes  or  insulators  are  used  as  the  bodies  to  be  charged. 
Equation  (3)  shows  that  when  the  distance  between  the 
two  opposed  conductors  is  diminished,  so  that  y  —  x  becomes 
small,  the  capacity  of  the  system  is  very  much  increased. 
This  is  equally  obvious  from  the  formula  for  the  capacity  of 
a  large  flat  plate  one  side  of  which  is  near  a  similar  un- 
insulated flat  plate,  and  separated  from  it  by  air,  while  the 
other  side  is  far  removed  from  all  conductors  ;  in  such  a 
case,  let  a  denote  the  distance  between  the  metallic  surfaces 
and  let  s  be  the  capacity/^-  unit  of  area,  then 

s  =  —  (4) 

47T0 

(IT  here  and  elsewhere  always  means  the  ratio  of  the  circumference 
to  the  diameter  of  a  circle  =  3-1416.  The  surface  of  a  sphere  of 
radius  unity  is  equal  to  4*-.) 


CHAP.  V.] 


Electro-static  Measiircment. 


97 


and  in  order  to  find  the  total  capacity  of  the  plate  we  may 
multiply  s  into  the  area  of  the  plate  with  sufficient  accuracy 
for  practical  purposes,  whenever  a  is  small  in  comparison 
with  this  area ;  a  must  be  measured  in  centimetres,  and 
the  surface  in  square  centimetres.  This  method  is  not  ab- 
solutely accurate,  because  at  the  edges  of  the  plates  the 
electricity  will  not  be  uniformly  distributed,  as  it  will  in  the 
middle  of  the  plate.  By  increasing  the  surface  and  diminish- 
ing a,  we  may  increase  indefinitely  the  quantity  which  the 
plate  or  conductor  will  contain  when  raised  to  a  given 
potential.  The  quantity  with  which  the  plates  will  be 
charged  with  a  given  potential  is  q  =  s  i  as  before. 

'  §  5.  The  arrangement  of  opposed  conductors  intended  to 
give  a  large  capacity  with  comparatively  small  surface  is 
termed  a  condenser.  The  capacity  of  a  condenser  depends 
on  the  dielectric  separating  the  conductors.  If  for  air  we 
substitute  gutta  percha,  the  capacity  will  be  increased  about 
four  and  a  quarter  times.  The  coefficient  by  which  the 
capacity  of  an  air  condenser  must  be  multiplied  in  order 
to  give  the  capacity  of  the  same  condenser  when  another 
dielectric  is  substituted  for  air  is  constant  for  each  substance, 
and  is  called  the  specific  inductive  capacity  of  the  dielectric. 
It  is  a  quantity  of  much  importance  in  telegraphy,  and  will 
in  this  treatise  be  designated  by  the  letter  K.  It  has  been 
approximately  determined  for  a  few  substances.  The  fol- 
lowing table  gives  the  numbers  for  these  : 


Air.  . 
Resin  . 
Pitch  . 
Beeswax 
Glass  . 
Sulphur 
Shellac 


Values  of  K. 

India  rubber 


77 
•80 
•86 
90 
•93 
•95 


2-5 


Hooper's  vulcanised  in- 

dia  rubber      .     .     .    =  3*1 
W.  Smith's  gutta  percha  =  3-59 
Gutta  percha      .     .     .    =  4*2 

Mica =5 

Paraffin    .....=  1-98' 


§  6.  The  numbers  are  approximate  values  only,  and,  in- 
1  Gibson  and  Barclay. 


H 


1« 


98  Electricity  and  Magnetism.          [CHAP.  v. 

deed,  extreme  accuracy  is  unattainable  on  account  of  the 
following  peculiarity  observed  in  all  solid  dielectrics.  When 
one  plate  A  of  the  condenser  is  first  raised  to  the  desired 
potential  by  contact,  say  with  one  electrode  c  of  a  galvanic 

battery,  the  other  elec- 
F|G- 56' trode   z  being  in  con- 
nection with  the  earth 
or  second  plate  of  the 
HZ;   condenser  as  in  Fig.  56, 
"To"  a  charge  rushes  in  with 

2F&—J      great  rapidity,  but  the 

entrance  of  the  elec- 
tricity does  not  instantly  cease,  as  is  the  case  with  an  air 
condenser;  on  the  contrary,  although  it  decreases  Very 
rapidly,  the  flow  of  electricity  into  the  condenser  does  not 
cease  for  many  hours.  This  phenomenon  has  already  been 
described  in  Chapter  IV.  §  10  in  its  bearing  on  currents. 
Similarly,  when  the  two  plates  are  joined  by  a  wire  so  as 
to  be  brought  to  one  potential,  the  electricity  is  discharged 
very  rapidly  at  first ;  but  this  discharge  is  so  far-  from 
being  completed  immediately  that  electricity  continues  to 
flow  out  for  precisely  as  long  a  time  as  it  ran  in,  and 
with  precisely  the  same  rapidity  after  each  interval  of 
time ;  i.e.  if,  upon  maintaining  a  difference  of  potential 
x  between  the  plates,  coatings,  or  armatures  (as  they  are 
often  called)  of  the  condenser,  a  quantity  q  per  second 
is  found  flowing  into  the  condenser  at  the  expiration  of 
thirty  minutes,  then  thirty  minutes  after  the  two  arma- 
tures have  been  joined,  or,  in  ordinary  language,  after 
the  condenser  has  been  discharged,  the  same  quantity 
q  per  second  will  be  found  flowing  from  one  armature  to 
the  other.  The  effect  produced  is  as  though  the  dielectric 
were  a  kind  of  sponge  absorbing  electricity  at  a  certain 
rate  when  subjected  to  a  certain  difference  of  potential, 
and  yielding  it  all  up  again  when  ihe  two  plates  were  brought 
to  one  potential.  A  condenser  with  glass  or  paraffin  be- 
tween the  armatures  has  not,  therefore,  the  same  definite 


CHAP.  ^.]          Electro-static  Measurement.  99 

capacity  as  an  air  condenser ;  the  capacity  is  generally 
understood  to  mean  the  capacity  for  receiving  electricity  from 
the  first  contact.  When  a  condenser  is  discharged,  if  con- 
tact be  not  maintained  between  the  armatures,  the  gradual 
restoration  of  this  quasi  absorbed  charge  raises  the  potential 
of  the  armature  which  had  previously  been  highly  charged, 
and  accumulates  upon  it,  so  that  on  again  making  contact 
between  the  armatures  a  second  considerable  discharge  is 
given,  and  a  succession  of  discharges  of  this  kind  can  be 
obtained  from  a  large  condenser  for  several  hours.  These 
are  called  residual  discharges.  The  same  law  holds  as  to 
charges ;  after  charging  the  armature  to  a  given  potential, 
and  leaving  it  insulated,  the  potential  gradually  falls,  owing 
to  the  absorption  by  the  glass  or  gutta  percha ;  then,  on 
raising  the  potential  of  the  armature  afresh,  by  connecting 
it  with  the  electrode  of  a  battery,  a  fresh  charge  can  be 
poured  into  the  condenser.  This  apparent  absorption  of  the 
electricity  by  the  dielectric  is  said  by  some  writers  to  be  due 
to  polarisation  caused  by  the  continued  electrification  of  the 
dielectric;  the  word  polarisation,  like  induction,  is  applied 
to  a  great  variety  of  phenomena  having  little  in  common. 

These  phenomena  are  readily  observed  in  a  condenser 
consisting  of  a  mile  of  telegraph  wire  insulated  by  gutta 
percha ;  the  copper  wire  is  the  one  armature  ;  if  the  gutta 
percha  be  covered  with  lead  or  tinfoil,  as  is  sometimes 
done,  this  forms  the  other  armature  ;  or,  if  the  gutta  percha 
covered  wire  be  placed  in  a  tub  of  water,  that  water  will  be 
the  second  armature.  With  a  sensitive  galvanometer  and 
a  battery  of  50  cells,  or  even  less,  all  the  phenomena  de- 
scribed are  easily  observed.  Condensers  of  smaller  bulk 
and  equal  capacity  can  be  obtained  from  the  makers  of  tele- 
graphic apparatus.  When  the  condenser  is  like  a  common 
glass- Leyden  jar  of  small  capacity,  and  insulated  with  a 
hard  material,  the  residual  discharges  may  be  observed  in 
the  form  of  a  succession  of  sparks  after  the  jar  has  been 
charged  to  a  high  potential  by  a  frictional  machine. 

II  2 


IOO  Electricity  and  Magnetism.         [C&AP.  v. 

§  7.  Let  a  small  flat  movable  plate  /,  supported  by  the 
torsion  of  a  wire  m  n  in  Fig.  57,  be  placed  flush  with  a  much 
FlG  57  larger  flat  fixed  plate  h  h 

surrounding  it  on  all 
sides,  and  let  both  plates 
be  placed  opposite  and 
parallel  to  a  third  unin- 
sulated plate  £",  then  if  a 
permanent  difference  of 
potentials  be  established 
in  any  way  between  g 

and  the  p.lates  <  and  /'' 

the  quantity  of  electricity 

per  unit  of  area  on  the  plate  f  will  be    — —  ,  and  the  elec- 

4  TT  a 

tricity  will  be  uniformly  distributed  over  the  plate/,  and  the 
electricity  of  the  opposite  sign  will  also  be  uniformly  distri-  • 
buted  over  the  opposing  surface  of  the  plate  g.  The  total 
force  with  which  the  plate/  is  attracted  by  g  will  be 

(5) 

Where  M  is  the  surface  of  the  plate  in  square  centimetres.1 
Apparatus  can  be  constructed  by  which  this  force  is  actually 
measured,  by  weighing  or  otherwise,  and  this  apparatus 
forms  an  absolute  electrometer  (Sir  William  Thomson's  guard 
ring  electrometer)  by  which  we  can  determine  the  difference 

of  potential  i  between  the  plates :  i  =  a    /  °  wf.  /  must 

M 

of  course  be  expressed  in  absolute  measure,  Chapter  V.  §  i. 
§  8.  Measured  by  apparatus  -  of  this  kind,  the   ordinary 
DanielPs  cell  (one  form  of  galvanic  battery)  is  found  to 
produce  a  difference  of  potentials  between  its  electrodes 
equal  to  "00374.     Experiment  showed  the  attraction  to  be 

1  Vide  paper  '  On  the  Mathematical  Theory  of  Electricity  in  Equili- 
brium, by  Sir  W.  Thomson.  Phil.  Mag.  1854,  second  half-year,  and 
republished  in  1872  in  a  volume  entitled  Electrostatics  and  Magnetism. 


CHAP.  V.]          Electro-static  Measurement* , , 


•05  7  grammes  per  square  centimetre  between  discs  separated 
by  -i  centimetre,  with  a  difference  of  potentials  produced  by 
1000  Daniell's  cells. 

Hence,  in  equation  (5),  if  the  weighings  had  taken  place 
in  Paris,  we  should  have  had  /=  980*868  x  '057  ;  but  in 
Glasgow  the  force  with  which  a  gramme  mass  weighs  is  less 
than  in  Paris,  so  that  /=  981-4  x  -057  =  55*94;  a  =  -i, 
and  M  =  i  ;  substituting  these  values  in  our  equation,  we 
obtain  /  =  3-74  for  1000  Daniell's  cells. 

Using  this  value  in  equation  4,  we  find  that  an  air  con- 
denser, with  a  square  metre  surface  and  the  plates  one 
millimetre  apart,  electrified  by  a  thousand  cells,  would  take 

a  charge  of  TOOOO  — 3jA —  ---2076  units.     If  the  plates 
4  TT  x  o'i 

had  been  separated  by  gutta  percha  instead  of  by  air, 
the  charge  on  the  plates  would  be  4*2  x  2976  =  12499,  the 
coefficient  4-2  being  the  specific  inductive  capacity  of  the 
material  taken  from  §  5. 

A  ball,  one  centimetre  in  diameter,  electrified  by  1000 
Daniell's  cells,  would  take  a  charge  of  -5  x  3*74,  or  1*87 
units  of  electricity. 

From  a  knowledge  of  this  quantity  we  may  calculate  the 
force  on  a  similar  ball  similarly  electrified,  but  so  far  off 
that  the  electricity  on  each  ball  would  remain  almost 
uniformly  distributed.  Two  such  balls  similarly  electrified 
at  a  distance  of  one  metre  would  repel  one  another  with  a 

force  =    - — '         — L  =  -00035   absolute  units  of  force 
10000 

(equation  i)  or  -000000357  grammes  weight.  When  the  balls 
are  brought  closer,  the  calculation  of  attractions  or  repulsions 
between  them  become  exceedingly  complicated,  owing  to  the 
redistribution  of  the  electricity  on  their  surface. 

§  9.  The  capacity  of  a  long  cylindrical  conductor  of  the 
diameter  */'and  length  L  enveloped  by  a  concentric  cylin- 
drical conductor  of  the  diameter  D,  and  separated  from  it 
by  an  insulator  with  the  specific  inductive  capacity  K  is 

/  s*9  S  -      >/       \^ 


IO2  -Electricity  and  Magnetism.  [CHAI\  V. 

K  L  K  L 


<-  J         4-6052  log  ° 


(6) 


(loge  signifies  that  natural  logarithms  are  to  be  employed  instead  of 
Napierian  logarithms. ) 

The  length  of  the  cylinder  is  assumed  to  be  so  great  that 
the  capacity  of  the  ends  may  be  neglected  ;  this  formula  is 
applicable  to  the  insulated  wire  used  for  submarine  cables. 
The  capacity  of  one  knot  of  the  English  Atlantic  cable  is 

f  =    4-2  x  6087  x  30-48   =      8oOQ  (centimbtres)> 

4-6052  x  log  3-28 

6087  is  the  number  of  feet  in  a  knot,  and  30-48  the  number 
of  centimetres  in  a  foot ;  3-28  is  the  ratio  between  the 
diameter  of  the  gutta-percha  and  that  of  the  wire  conductor. 
It  follows  from  the-  above,  that  the  charge  per  knot  of 
this  cable  when  electrified  by  100  Darnell's  cells  is  '374 
x  328000  =  1 22670  and  every  time  the  cable  is  charged  or 
discharged  this  quantity  per  knot  flows  in  and  out ;  thus  if 
•oi  second  be  occupied  in  charging  200  knots  the  mean 
strength  of  the  current  flowing  for  goi  second  will  be 

122670  x  200  .,      f 

— '- =  245340  units  of  current. 

§  10.  The  term  electric  density  signifies  the  quantity  of 
electricity  per  square  centimetre  on  a  charged  conductor. 
The  equations  (2),  (3),  and  (4)  allow  us  to  calculate  this  for 
spheres  and  condensers  with  flat  plates  ;  equation  (4)  is 
applicable  to  any  form  of  condenser  in  which  the  curva- 
ture is  not  considerable  relatively  to  the  thickness  a  of  the 
dielectric.  It  is  applicable,  therefore,  to  the  ordinary  Leyden 
jar,  with  the  simple  modification  that  the  value  obtained 
from  it  must  be  multiplied  by  the  number  expressing  the 
specific  inductive  capacity  of  the  dielectric.  The  electri- 
cal attraction  or  repulsion,  exerted  on  a  small  quantity  q 
of  electricity  close  to  an  electrified  surface,  is  easily  calcu- 
lated when  the  electric  density  on  the  surface  p  is  known. 
It  is  perpendicular  to  the  surface,  and  in  air  is  equal  to 

47TP?   =    R?  (7) 


CHAP.  V.]          Electro-static  Measurement.  103 

where  R  is  the  electrostatic  force  close  to  the  surface,  i.e.  the 
force  which  the  charge  would  exert  per  unit  of  quantity  on 
the  small  charge  q. 

Between  two  parallel  opposed  conducting  surfaces,  differ- 
ing in  potential  by  the  amount  z,  and  separated  by  a  small 
distance  compared  with  their  size,  the  resultant  electro- 
static force  R  tends  to  impel  any  small  quantity  of  electricity 
straight  across  from  one  surface  to  the  other,  in  a  direction 
perpendicular  to  the  surface,  with  a  force  /  which  is  constant 
in  amount.  Retaining  the  previous  notation  we  have 

/=  R^r  =  L  q  (8) 

a 

The  work  done  on  q  in  crossing  is  fa  =  /  q. 

The  electric  density  on  a  small  sphere  at  a  given  potential 
is  much  greater  than  on  a  large  one,  for  the  capacity  in- 
creases only  as  the  radius,  while  the  area  increases  as  the 
square  of  the  radius;  hence  an  infinitely  small  sphere 
charged  to  any  sensible  potential  would  have  an  infinitely 
great  electric  density  on  its  surface,  and  the  force  it  would 
exert  on  electricity  in  its  immediate  neighbourhood  would 
be  infinitely  great ;  it  would,  in  fact,  repel  its  own  parts 
infinitely,  and  we  may  therefore  infer  that  it  would  be 
impossible  to  charge  a  very  small  sphere  to  a  very  high 
potential.  This  inference  is  justified  by  experiment.  The 
distribution  of  electricity  over  bodies  which  have  points  or 
angles  is  such  that  the  electric  density  becomes  very  great 
on  these  points,  as  it  would  on  a  very  small  sphere,  even 
when  the  potential  is  not  high.  The  result  is  a  great 
repulsion  of  the  electricity  for  itself,  or  rather  a  great  re- 
pulsion between  neighbouring  parts  of  the  matter  charged 
with  it;  we  then  frequently  see  the  electrified  matter 
passing  off  in  the  condition  known  as  an  electric  spark, 
or  as  what  is  termed  an  electric  brush.  Anything  tend- 
ing to  produce  a  great  density  at  any  part  of  the  surface 
of  a  charged  conductor  tends  to  produce  the  s*park.  Thus 
by  approaching  a  finger  to  a  charged  conductor,  the  density 


104 


Electricity  and  Magnetism.          [CHAP.  V. 


is  increased  by  induction  opposite  the  finger,  and  may  be  in- 
creased sufficiently  to  produce  the  spark.  Increased  electric 
density  by  no  means  necessarily  implies  increase  of  potential 
unless  the  form  and  position  of  the  conductors  are  constant. 
§  11.  There  is  a  real  diminution  of  air-pressure  against 
the  surface  of  a  charged  conductor,  due  to  the  repulsion  of 
the  electricity  for  itself.  This  mechanical  force  can  be 
made  evident  by  electrifying  a  soap-bubble,  which  expands 
when  electrified,  and  collapses  when  discharged.  If  the 
air-pressure  per  square  centimetre  be  called/,  we  have 

p    =    2    7T  p2  (9) 

The  diminution  of  air-pressure  required  before  a  spark  takes 
place  between  two  slightly  convex  parallel  plates  has  been 
tested  by  Sir  William  Thomson,  with  the  results  shown  in 
the  following  table  : 


Pressures  of 

Length  of  .sparks 
in  centimetres 

=  A 

Electrostatic 
force  R  close  to 
surface  in  abso- 
lute units. 
Vide  §  10. 

Electromotive 
force  =  R  x  A, 
or    difference    of 
potential, 
which  produced  a 
spark 
of  length   A. 

electricity  from 
either  surface  im- 
mediately before 
disruption  in 
grammes  weight 
per  square 
centimetre  = 

R2 

877X98  1  '4. 

•00254 

5277 

i'34 

II-290 

•00508 

367-8 

1-87 

5'49 

•0086 

26yi 

2-30 

2-89 

•OIQO 

224-2 

4-26 

2-O4 

•0408 

IS^S 

6-19 

•931 

•0688 

I4O'8 

9-69 

•806 

•1325 

131 

I7-35 

•696 

It  is  curious  to  observe  that  the  electrostatic  force  is  not 
constant,  as  might  have  been  expected ;  and  that  the  electro- 
motive force  required  to  produce  a  spark  does  not  increase 
in  simple  proportion  to  the  length  of  the  spark,  being  less 
per  unit  of  distance  between  the  opposed  surfaces  for  long 
sparks  than  for  short  ones.  It  follows  from  the  measurement  in 
§  8,  that  2,600  Darnell's  cells  would  produce  a  spark  of  -0688 


CHAP,  v.]         Electro-static  Measurement.  105 

centimetres  between  two  very  slightly  convex  surfaces  :  by 
observing  the  length  of  spark,  which,  under  similar  circum- 
stances, can  be  obtained,  say,  from  a  Leyden  jar,  we  may 
roughly  estimate  the  potential  to  which  it  has  been  charged. 
§  12.  The  brushes  or  sparks  which  fly  off  from  points 
charged  to  high  potentials,  show  that  in  all  apparatus  in- 
tended to  remain  charged  at  a  high  potential,  every  angle 
and  point  must  be  avoided  on  the  external  surfaces.  It  is 
easy  to  draw  off,  by  a  silent  and  invisible  discharge  from  a 
point,  by  far  the  greatest  part  of  the  charge  of  a  conductor 
without  any  direct  contact  with  the  discharging  conductor  : 
points  are  also  spoken  of  as  collecting  electricity  from  any 
electrified  body  held  in  the  neighbourhood  ;  their  action  is  as 
follows  :  If  attached  to  an  insulated  conductor,  and  held  near 
an  electrified  body  A,  they  become  charged  by  induction  with 
the  opposite  kind  of  electricity.  This  flies  off  in  sparks,  or 
by  a  silent  discharge,  and  leaves  the  insulated  conductor 
charged  with  the  same  electricity  as  that  contained  in  A.  This 
property  of  points  explains  the  action  of  lightning  conductors. 
Lightning  is  an  enormous  electric  spark  passing  between 
two  clouds,  or  from  a  cloud  to  the  earth  ;  in  the  latter  case 
the  electrified  cloud  is  attracted  towards  any  prominence  or 
good  conductor,  which  becomes  electrified  by  induction,  and 
the  spark  of  lightning  passes  when  the  difference  of  poten- 
tials is  sufficient  to  overcome  the  mechanical  resistance  of 
the  air.  If  the  electrified  prominence  on  the  earth  be 
armed  with  a  point  connected,  by  good  conductors,  such  as 
large  copper  rods,  with  the  earth,  then,  as  soon  as  the  po- 
tential of  the  point  is  raised  even  slightly,  the  electricity 
passes  off  from  the  point  into  the  air ;  the  prominence  can 
no  more  be  electrified  highly  by  induction  than  a  leaky 
bucket  can  be  filled  with  water ;  the  electrified  clouds  are 
not  attracted  to  the  neighbourhood,  and  even  should  they 
be  driven  there  in  such  quantity  that  the  electricity  flying 
off  from  the  point  is  insufficient  to  prevent  a  spark  from 
passing,  the  spark  will  pass  from  the  cloud  to  the  point, 


Io6  Electricity  and  Magnetism.          [CHAP.  V, 

inasmuch  as  the  electric  density  and  attraction  will  be 
greater  there  than  anywhere  in  the  neighbourhood.  Elec- 
tricity conveyed  by  a  good  metal  conductor  to  the  earth 
does  no  harm,  and  leaves  no  trace  of  its  passage  ;  whereas, 
a  spark  driven  through  an  insulator  or  bad  conductor,  tears 
it  to  pieces  on  its  passage;  this  fact  may  be  verified  by 
sending  a  spark  through  glass,  which  will  be  cracked  and 
shivered,  or  through  paper,  which  will  have  a  hole  torn  in 
it.  The  electromotive  force  required  to  produce  mechanical 
results  of  this  character  is  much  greater  than  that  required 
to  open  a  passage  through  a  corresponding  thickness  of  air. 
We  may,  therefore  frequently,  prevent  the  passage  of  sparks 
between  two  conductors,  by  covering  one  of  them  with 
ebonite,  glass,  or  other  hard  insulator. 

Sir  W.  Thomson  has  found  that  if  a  conductor  with  sharp 
edges  or  points  is  surrounded  by  another,  presenting  every- 
where a  smooth  surface,  a  much  greater  difference  of  poten- 
tial can  be  established  between  them  without  producing 
disruptive  discharge,  when  the  points  and  edges  are  positive, 
than  when  they  are  negative. 

§  13.  The  distribution  of  electricity  over  opposing  sur- 
faces, when  these  are  not  of  the  simplest  description,  offers 
problems  of  extreme  complication.  Generally,  we  know 
that  the  density  will  be  greatest  where  the  opposing  con- 
ductors are  close  together,  and  where  they  have  angles  or 
points,  that  it  will  increase  directly  as  the  difference  of 
potential  and  directly  as  the  specific  inductive  capacity  of 
the  dielectric.  We  must  especially  remember  that  the  charge 
or  electric  density  on  opposed  surfaces  depends  on  differ- 
ence of  potential,  and  not  on  absolute  potential,  so  that  on 
electrifying  the  outside  of  a  charged  insulated  Leyden  jar,, 
we  shall  raise  not  only  the  potential  of  the  outer,  but  also 
that  of  the  inner  coating  ;  from  the  same  cause  the  charge 
of  any  condenser  due  to  contact  with  two  electrodes  of  a 
battery  will  be  the  same,  whether  one  electrode  of  the  battery 
be  uninsulated  or  not,  i.e.  the  quantity  which  will  flow  from 


CHAP,  v.]  Electro-static  Measurement.  107 

one  armature  to  the  other  when  joined  will  be  unaltered, 
but  the  quantity  flowing  from  either  armature  to  the  earth 
will  depend  on  the  potential  of  that  armature.  Any  change 
in  the  total  quantity  of  a  charge  on  a  conductor  will  change 
its  potential  as  a  change  of  its  potential  will  change 
the  charge.  Putting  a  charged  conductor  in  contact  with 
another  conductor  at  the  same  potential,  will  not  alter  the 
distribution  of  the  charge  in  either ;  but  if  two  conductors 
at  different  potentials  are  brought  into  contact,  there  must 
necessarily  be.  a  redistribution  of  the  charge  due  to  the  inter- 
mediate potential  assumed  by  the  two  bodies.  Mr.  F.  C. 
Webb  in  his  treatise  on  electrical  accumulation  and  con- 
duction, has  given  many  instructive  examples  of  the  dis- 
tribution of  electricity  under  different  circumstances.  The 
theory  already  stated  explains  his  results. 

§  14.  The  simple  laws  connecting  potential,  quantity, 
capacity,  density,  and  electrical  attraction  or  repulsion  have 
now  been  stated,  and  the  nature  of  the  measurements  has 
been  indicated,  by  which  potential,  quantity,  and  capacity  can 
be  defined  in  terms  of  length,  mass,  and  time  ;  a  current  is 
necessarily  measured  by  measuring  the  quantity  which  passes 
per  second,  and  resistances  are  expressed  in  terms  of  that 
resistance  which  would  allow  the  unit  current  to  pass  in  the 
unit  of  time,  with  tlieunit  electromotive  force  acting  between 
the  two  ends  of  the  wire.  To  give  some  idea  of  the 
material  representation  of  units  of  this  kind,  it  may  be  stated 
that  this  resistance  would  be  represented  by  about  one 
hundred  million  kilometres  of  mercury  at  o°  Centigrade,  in 
a  tube,  the  sectional  area  of  which  was  one  thousandth  of  a 
square  millimetre  ;  electricians  when  they  measure  the  resist- 
ance of  the  gutta  percha  envelope  of  a  mile  of  cable,  ob- 
serve resistances  of  about  ^uVo-th  °f  tm's  magnitude ;  approxi- 
mately the  insulation  resistance  of  one  foot  of  gutta-percha 
covered  wire  is  of  about  this  magnitude.  The  unit  of  current 
is  such  as  would  be  given  by  a  battery  of  about  268  Daniell's 
cells  through  the  above  resistance.  The  unit  quantity  of  elec- 


io8  Electricity  and  Magnetism.         [CHAP.  v. 

tricity  is  that  on  a  sphere  two  centimetres  diameter,  elec- 
trified by  one  pole  of  268  Daniell's  cells  in  series,  the  other 
pole  being  in  connection  with  the  earth.  This  quantity 
discharged  per  second  would  give  a  current  equal  in 
strength  to  that  flowing  through  the  long  mercury  conductor 
or  gutta  percha  envelope  from  the  268  cells.  This  series  of 
units  is  called  the  electrostatic  absolute  centimetre-gramme, 
second  series.  This  electrostatic  series  is  the  most  con- 
venient for  calculations  concerning  electricity  at  rest,  but 
when  treating  of  currents  and  magnets,  a  distinct  series  of 
units  is  used  ;  this  double  series  of  units  involves  no  greater 
inconvenience  than  the  use  of  the  chain,  acre,  and  rod  for 
surveying,  while  the  inch,  foot,  and  square  inch  are  used  to 
describe  machinery. 

§  15.  The  four  principal  electrostatic  units  are  directly 
determined  by  four  fundamental  equations  ;  from  equation 

(i),  §  3,  we  have/=   ^^,  from  which,  if  q^  =  q,  we  directly 

find  the  unit  of  quantity  in  terms  of  the  unit  of  force  ;  we 
know  by  the  definition  of  potential  that  the  work  so  done 
in  conveying  the  quantity  q  .of  electricity  between  two 
points  at  potentials  differing  by  the  amount  /  is  equal  to 
q  i  or 


This  gives  the  unit  difference  of  potentials  in  terms  of  q  and 
the  unit  of  work;  by  definition   §    14  the  current  c  =  3- 

where  q  is  the  quantity  passing  in  the  time  t,  and  from  this 
equation  we  obtain  the  unit  of  current  in  terms  of  ^,  and  the 

unit  of  time;  from  Ohm's  law  r  =  —  ,  by  which  we  obtain 

the  unit  of  resistance  in  terms  of  i  and  c. 

Finally,  the  unit  of  capacity  is  directly  derived  from  that 
of  potential  and  quantity  ;  the  unit  of  density  from  that  of 
surface  and  quantity. 


CHAP.  VI.]  Magnetism.  109 

If  the  capacity  of  a  conductor  be  called  s,  we  have  s  =  -C, 

where  q  is  the  quantity  with  which  it  is  charged  by  the 
electromotive  force  i. 


CHAPTER  VI. 

MAGNETISM. 

§  1 .  A  MAGNET  in  the  popular  acceptation  of  the  word  is  a 
piece  of  steel,  which  has  the  peculiar  property,  among  others, 
of  attracting  iron  to  its  ends.  Certain  kinds  of  iron  ore 
called  loadstone  have  the  same  properties. 

If  a  magnet  A  be  free  to  turn  in  any  direction,  the  pre- 
sence of  another  magnet  B  will  cause  A  to  set  itself  in  a 
certain  definite  position  relatively  to  B.  The  position  which 
one  magnet  tends  to  assume  relatively  to  another,  is  con- 
veniently defined  in  terms  of  an  imaginary  line,  occupying 
a  fixed  position  in  each  magnet,  and  which  we  will  call  the 
magnetic  axis.  The  greatest  manifestation  of  force  exerted 
by  a  long  thin  magnet,  is  found  to  occur  near  its  ends,  and 
the  two  ends  of  any  one  such  magnet  possess  opposite 
qualities ;  this  peculiarity  has  caused  the  name  of  poles  to 
be  given  to  the  ends  of  long  thin  magnets.  These  poles 
are  commonly  looked  upon  as  centres  offeree,  but  except 
in  the  case  of  long,  infinitely  thin,  and  uniformly  magnetised 
rods  they  cannot  be  considered  as  simple  points  exerting 
forces  ;  nevertheless,  the  conception  of  a  magnet  as  a  pair 
of  poles,  capable  of  exerting  opposite  forces,  joined  by  a 
bar  exerting  no  force,  is  so  familiar,  and  in  many  cases  so 
nearly  represents  the  facts  that  it  will  be  employed  in 
this  treatise.  The  magnetic  axis,  as  above  defined,  is  the 
line  joining  the  two  imaginary  poles. 

§  2.  Every  magnet,  if  free  to  turn,  takes  up  a  definite 
position  relatively  to  the  earth,  which  is  itself  a  magnet.  The 


no  Electricity  and  Magnetism.        [CHAP.  VI. 

pole,  which  in  each  magnet  turns  to  the  north,  will  by  us  be 
called  the  north  pole  of  the  magnet.  The  other  pole  will 
be  called  the  south  pole.  The  two  north  poles  of  any  two 
magnets  repel  one  another ;  so  do  the  two  south  poles  ;  but 
any  north  pole  attracts  any  south  pole.  Hence,  the  north 
pole  of  a  magnet  is  similar  in  character  to  the  south  end  of 
the  earth.  The  pole  which  is  similar  to  the  south  end  of 
the  earth  is  sometimes  called  the  positive  pole ;  the  other, 
which  we  call  the  south  pole  of  the  magnet,  is  the  negative 
pole.  When  a  magnet  is  broken  each  piece  forms  a  com- 
plete magnet  with  a  north  and  south  pole. 

§  3.  The  strength  of  a  pole  is  necessarily  denned  as  propor- 
tional to  the  force  which  it  is  capable  of  exerting  on  another 
given  pole;  hence  the  force/  exerted  between  two  poles  of 
the  strengths  m  and  ml  must  be  proportional  to  the  product 
m  mv  The  force/ is  also  found  to  be  inversely  proportional 
to  the  square  of  the  distance  D,  separating  the  poles,  and  to 
depend  on  no  other  quantity;  hence,  choosing  our  units 
correctly,  we  have 

/=  ^  (•) 

The  strength  of  a  pole  is  a  magnitude  which  must  be 
measured  in  terms  of  some  unit.  When  in  the  above 
equation  we  make /and  D  both  equal  to  unity,  the  product 
m  ml  must  also  be  equal  to  unity  hence  from  equation  (i)  it 
follows  that  the  unit  pole  is  that  which  at  the  unit  distance 
repels  another  similar  and  equal  pole  with  unit  force. 

/will  be  an  attraction  or  a  repulsion  according  as  the 
poles  are  of  opposite  or  similar  kinds.  The  number  m  is 
positive  if  it  measures  the  strength  of  a  north  pole  and 
negative  if  it  measures  the  strength  of  a  south  pole ;  hence  an 
attracting  force  will  be  affected  with  the  negative  sign,  and 
a  repelling  force  with  the  positive  sign. 

§  4.  We  observe  that  the  presence  of  the  magnet  in  some 
way  modifies  the  surrounding  region,  since  any  other  magnet 
brought  into  that  region  experiences  a  peculiar  force.  The 


CHAP.  VI.]  Magnetism.  in 

neighbourhood  of  a  magnet  is  often  for  convenience  called 
a  magnetic  field  ]  and  for  the  same  reason  the  effect  pro- 
duced by  a  magnet  is  often  spoken  of  as  due  to  the  mag- 
netic field  instead  of  to  the  magnet  itself.  This  mode  of 
expression  is  the  more  proper,  inasmuch  as  the  same  or  a 
similar  condition  of  space  is  produced  by  the  passage  of 
electric  currents  in  the  neighbourhood,  without  the  presence 
of  a  magnet.  Since  the  peculiarity  of  the  magnetic  field 
consists  in  the  presence  of  a  certain  force,  we  may  numerically 
express  the  properties  of  the  field  by  measuring  the  strength 
and  direction  of  the  force,  or,  as  it  may  be  worded,  the 
intensity  of  the  field,  and  the  direction  of  the  lines  of  force. 

This  direction  at  any  point  is  the  direction  in  which  the 
force  tends  to  move  a  free  pole ;  and  the  intensity  H  of  the 
field  is  defined  as  proportional  to  the  force  f,  with  which 
it  acts  on  a  free  pole  ;  but  this  force  f  is  also  proportional 
to  the  strength  m  of  the  pole  introduced  into  the  field, 
and  it  depends  on  no  other  quantities  ;  hence, 

/  =  m  H          k— -•  (2) 

and  therefore  the  field  of  unit  intensity  will  be  that  which 
acts  with  unit  force  on  the  unit  pole. 

§  5.  The  lines  offeree  produced  by  a  long  thin  bar  magnet 
near  its  poles  radiate  from  the  poles  ;  the  intensity  of  the 
field  is  equal  to  the  quotient  of  the  strength  of  the  pole 
divided  by  the  square  of  the  distance  from  the  pole;  thus 
the  unit  field  will  be  produced  at  the  unit  distance  from  the 
unit  pole. 

In  a  uniform  magnetic  field,  the  lines  of  force  will  be 
parallel ;  such  a  field  can  only  be  produced  by  special 
combinations  of  magnets,  but  a  small  field  at  a  great 
distance  from  the  pole  producing  it  will  be  sensibly 
uniform.  Thus  in  any  room  unaffected  by  the  neighbour- 
hood of  iron  or  magnets,  the  magnetic  field  due  to  the 
earth  will  be  sensibly  uniform  :  its  direction  being  that 
assumed  by  the  dipping  needle.  The  dipping  needle  is  a 


112  Electricity  and  Magnetism.        [CHAP.  vi. 

long  magnet  supported  in  such  a  way  as  to  be  free  to  take 
up  its  position  as  directed  by  the  earth,  both  in  a  horizontal 
and  vertical  plane  ;  it  requires  to  be  very  perfectly  balanced 
before  being  magnetised,  otherwise  gravitation  will  prevent 
it  from  freely  obeying  the  directing  force  of  the  earth's 
magnetism. 

§  6.  We  can  never  really  have  a  single  pole  of  a  magnet 
entirely  free  or  disconnected  from  its  opposite  pole,  but  from 
the  effect  which  would  be  produced  on  a  single  pole  it  is 
easy  to  deduce  the  effect  produced  by  a  magnetic  field  on  a 
real  bar  magnet.  In  a  uniform  field,  two  equal  opposite  and 
parallel  forces  act  on  the  two  poles  of  the  bar  magnet,  and 
tend  to  set  it  with  its  axis  in  the  direction  of  the  force  of  the 
field.  This  pair  of  forces  tending  to  turn  the  bar,  but  not 
to  give  it  any  motion  of  translation,  constitutes  what  is 
termed  in  mechanics  a  couple.  When  the  magnet  is  so 
placed  that  its  axis  is  at  right  angles  to  the  lines  of  force 
in  the  field,  this  couple  G  is  proportional  to  the  intensity  of 
the  field  H,  the  strength  of  the  poles  #z,  and  the  distance 
between  them  / ;  or 

G  =  m  I  H  (3) 

The  product  m  I  is  called  the  magnetic  moment  of  the 
magnet ;  and  from  equation  (3),  it  follows  that  the  moment 
of  any  given  bar  magnet  is  measured  by  the  couple  which  it 
would  experience  in  a  field  of  unit  intensity,  when  it  is 
placed  normal  to  the  lines  of  force.  A  couple  is  measured 
by  the  product  of  one  of  its  forces  multiplied  into  the 
distance  between  them.  The  intensity  of  magnetisation  of  a 
magnet  is  the  ratio  of  its  magnetic  moment  to  its  volume. 

§  7.  When  certain  bodies  (notably  soft  iron)  are  placed 
in  a  magnetic  field  they  become  magnetised,  the  axis  joining 
their  poles  being  in  the  same  direction  as  would  be  assumed 
by  the  axis  of  a  free  steel  magnet  in  the  same  part  of  the 
field.  Thus  if  the  small  pieces  of  soft  iron  n  s  are  magnet- 
ised by  the  action  of  the  magnet  N  s  producing  the  lines  of 


CHAP.  VL] 


Magnetism. 


force  shown  in  Fig.  58,  the  north  pole  will  be  near  n,  the 
south  pole  near  s  in  each  case.  Magnetisation  when  pro- 
duced in  this  way  is  said  to  be  induced,  and  the  action  is 
called  magnetic  induction.  The  intensity  of  the  magnetisa- 
tion (except  when  great)  is  nearly  proportional  to  the  in- 
tensity of  the  field.  We  have  seen  in  Chapter  III.  §  13,  that 
soft  iron,  round  which  a  current  of  electricity  circulates, 
becomes  magnetised.  When,  therefore,  we  can  calculate  the 
intensity  of  the  magnetic  field  which  we  now  see  is  produced 
by  the  electric  current,  we  shall  be  able  to  calculate  the 
intensity  of  magnetisation  of  the  soft  iron  core.  When  the 
magnetisation  approaches  the  limiting  intensity  which  the 
soft  iron  is  capable  of  receiving,  it  always  falls  short  of  that 
calculated  on  this  principle. 

Bodies  in  which  the  direction  of  magnetisation  is  the  same 
as  that  of  the  field  are  termed  paramagnetic.  Iron,  cobalt, 
and  nickel,  chromium  and  manganese,  are  paramagnetic ; 
some  compounds  of  iron  are  also  paramagnetic.  Some 
of  these  bodies  retain  their  magnetism,  so  that  we  can 

FIG.  58. 


have  an  independent  nickel  magnet.  Iron  is  capable  of 
much  more  intense  magnetisation  than  nickel,  but  nickel 
approaches  iron  in  this  respect  more  nearly  than  any  other 
material.  Certain  other  materials,  such  as  bismuth,  anti- 
mony, and  zinc,  are  magnetised  by  a  magnetic  field,  so  that 

I 


114  Electricity  and  Magnetism.         [CHAP.  VI. 

the  direction  of  magnetisation  is  opposite  to  that  of  the 
field  :  they  are  called  diamagnetic.  None  of  these  bodies 
can  be  so  intensely  magnetised  as  iron,  nor  do  they  retain 
their  diamagnetism  when  removed  from  the  field. 

§  8.  One  consequence  of  magnetic  induction  is  that  when 
a  number  of  similar  magnets  are  laid  side  by  side  we  obtain 
a  compound  magnet  stronger  indeed  than  any  of  the  com- 
ponent magnets,  but  much  less  strong  than  the  sum  of  the 
strengths  of  the  separate  magnets  used.  For  when  a  magnet 
N  s  is  brought  near  another  N'  s',  as  in  Fig.  59,  the  north  pole 
N  tends  to  induce  a  south  pole  at  N'  and  similarly  N'  tends  to 
induce  a  south  pole  at  N.  The  result  is  that  N  and  N'  by 
FIG.  59.  FIG.  60. 


their  mutual  action  weaken  one  another,  if  N  be  sufficiently 
strong  relatively  to  N',  it  may  actually  reverse  the  polarity  ot 
the  weak  magnet.  If  on  the  other  hand  two  equal  magnets 
are  placed,  as  in  Fig.  60,  N  and  s'  mutually  strengthen  one 
another  by  induction,  but  since  they  tend  to  induce  opposite 
and  equal  magnetic  fields  the  result  is  to  weaken  the  re- 
sultant field  in  the  neighbourhood,  and  if  the  magnets  are 
allowed  to  touch,  the  strength  of  the  field  will  be  reduced 
to  an  insensible  amount.  When  the  magnets  are  not  equal 
the  weaker  magnet  will  reduce  the  strength  of  the  magnetic 
field  due  to  the  stronger. 

§  9.  When  soft  iron  is  magnetised  by  being  placed  in  a 
magnetic  field  a  sensible  time  elapses  before  it  assumes  the 
maximum  intensity  of  magnetisation  which  the  field  will 
produce.  Similarly,  when  the  bar  of  soft  iron  is  withdrawn 
from  the  field  it  does  not  lose  its  magnetism  instantly  ;  the 
magnetism  decreases  as  gradually  as  it  increased,  and  in 
almost  all  cases  some  traces  of  magnetism  will  remain  for 


CHAP.  VI.]  Magnetism.  115 

hours  or  perhaps  for  ever  after  the  iron  has  been  withdrawn 
from  the  magnetic  field.  This  remnant  of  magnetisation  is 
often  called  residual  magnetism  ;  most  ordinary  pieces  of  iron 
show  residual  magnetism  very  distinctly,  especially  in  large 
masses;  but  very  perfectly  annealed  iron  of  certain  qualities 
shows  very  little,  and  is  valuable  on  that  account  in  the  con- 
struction of  telegraph  instruments.  The  cause  of  this  phe- 
nomenon is  called  coercive  force.  The  slowness  with  which 
iron  in  any  mass  gains  or  loses  its  magnetism  is  a  serious 
impediment  to  the  construction  of  quick-working  telegraphic 
apparatus.  The  term  '  soft  iron '  is  applied  to  denote  iron 
which  loses  its  magnetism  rapidly,  or  in  -  other  words  iron 
which  has  little  coercive  force. 

§  10.  The  conception  of  electric  potential  has  been  ex- 
plained at  length  in  Chapter  II.  Magnetic  potential  is  an 
analogous  conception.  If  we  move  a  single  magnetic  pole 
from  one  point  to  another  of  the  magnetic  field,  we  shall 
find  that  the  forces  in  the  field  perform  work  on  the  pole,  or 
that  they  act  as  a  resistance  to  its  motion  according  as  the 
motion  is  with,  or  contrary  to,  the  forces  acting  on  the  pole; 
if  the  pole  moves  at  right  angles  to  the  force,  no  work  is 
done.  The  difference  of  magnetic  potential  between  any  two 
points  of  the  field  is  measured  by  the  work  done  by  the 
magnetic  forces  on  a  unit  pole  moved  against  them  from 
the  one  point  to  the  other,  supposing  the  unit  pole  to 
exercise  no  influence  on  the  field  in  question.  A  point 
infinitely  distant  from  the  pole  of  any  magnet  must  be  at 
zero  magnetic  potential,  and  hence  the  magnetic  potential  of 
any  point  in  the  field  is  measured  by  the  work  done  by  the 
magnetic  forces  on  a  unit  pole  during  its  motion  from  a 
point  infinitely  far  off  from  all  magnets  to  the  point  in 
question,  with  the  same  limitation  as  before. 

An  equipotential  surface  in  a  magnetic  field  is  a  surface 
so  drawn  that  the  magnetic  potential  at  all  its  points  shall  be 
the  same.  By  drawing  a  series  of  equipotential  surfaces,  cor- 
responding to  the  potentials  i,  2,  3  .  .  .  n,  we  may  map 

I  2 


1 1 6  Electricity  and  Magnetism.         [CHAP.  VI. 

out  any  magnetic  field  so  as  to  indicate  its  properties.  The 
unit  pole  in  passing  from  one  such  surface  to  the  next  against 
the  magnetic  forces  will  always  perform  one  unit  of  work. 

The  direction  of  the  magnetic  force  at  any  point  is  per- 
pendicular to  the  equipotential  surface  at  that  point ;  its 
intensity  is  the  reciprocal  of  the  distance  between  one  sur- 
face and  the  next  at  that  point ;  i.e.  if  the  distance  from 
surface  to  surface  be  £,  measured  in  units  of  length,  the  in- 
tensity of  the  field  will  be  4. 

§  11.  The  magnetic  field  may  be  mapped  out  in  another 
manner :  this  second  method  is  due  to  Faraday. 

Let  a  line  whose  direction  at  each  point  coincides  with  that 
of  the  force  acting  on  the  .pole  of  a  magnet  at  that  point  be 
called  a  line  of  magnetic  force.  By  drawing  a  sufficient 
number  of  such  lines  we  may  indicate  the  direction  of  the 
force  in  every  part  of  the  magnetic  field ;  but  by  drawing 
them  according  to  a  certain  rule  we  may  also  indicate  the 
intensity  of  the  force  at  any  point  as  well  as  the  direction.  It 
has  been  shown  *  that  if  in  any  point  of  their  course  the 
number  of  lines  passing  through  a  unit  area  is  proportional 
to  the  intensity  there,  the  same  proportion  between  the 
number  of  lines  in  a  unit  of  area  and  the  intensity  will  hold 
good  in  every  part  of  the  course  of  the  lines. 

If,  therefore,  we  space  out  the  lines  so  that  in  any  part 
of  their  course  the  number  of  lines  which  start  from  unit  of 
area  is  numerically  equal  to  the  number  measuring  the  in- 
tensity of  the  field  there,  then  the  intensity  at  any  other  part 
of  the  field  will  also  be  numerically  equal  to  the  number  of 
lines  which  pass  through  unit  of  area  there ;  so  that  each 
line  indicates  a  constant  and  equal  force. 

The  lines  of  force  are  everywhere  perpendicular  to  the 
equipotential  surfaces  ;  and  the  number  of  lines  passing 
through  unit  of  area  of  an  equipotential  surface  is  the  re- 
ciprocal of  the  distance  between  that  equipotential  surface 

1  Vide  Maxwell  on  'Faraday's  Lines  of  Force,'  Cambridge  Phil. 
Trans.  1857. 


CHAP.  VI.]  Magnetism.  117 

and  the  next  in  order — a  statement  made  above  in  slightly 
different  language. 

§  12.  In  a  uniform  field  the  lines  of  force  are  straight, 
parallel,  and  equidistant,  and  the  equipotential  surfaces  are 
planes  perpendicular  to  the  lines  of  force,  and  equidistant 
from  each  other. 

If  one  magnetic  pole  of  strength  m  be  alone  in  the  field 
its  lines  of  force  are  straight  lines,  radiating  from  the  pole 
equally  in  all  directions,  and  their  number  is  4  TT  m.  The 
equipotential  surfaces  are  a  series  of  spheres  whose  centres 
are  at  the  pole  and  whose  radii  are  m,  ^m,  %m,  \m,  &c.  In 
other  magnetic  arrangements  the  lines  and  surfaces  are 
more  complicated. 

Since  a  current  exerts  a  force  on  the  pole  of  a  magnet 
in  its  neighbourhood  it  may  be  said  to  produce  a  mag- 
netic field,  and  we  may  draw  magnetic  lines  of  force  and 
equipotential  surfaces  depending  on  the  form  of  the  circuit 
conveying  the  current,  and  the  strength  of  that  current. 
When  the  current  is  a  straight  line  of  indefinite  length  like 
a  telegraph  wire,  a  magnetic  pole  in  its  neighbourhood  is 
urged  by  a  force  tending  to  turn  it  round  the  wire,  so  that  at 
any  given  point  the  force  is  perpendicular  to  the  plane  pass- 
ing through  this  point  and  the  axis  of  the  current.  The  equi- 
potential surfaces  are  therefore  a  series  of  planes  passing 
through  the  axis  of  the  current  and  inclined  at  equal  angles 
to  each  other.  If  the  unit  current  be  defined  as  that  current, 
the  unit  length  of  which  acts  with  unit  force  on  the  unit 
magnetic  pole  at  the  unit  distance,  then  the  number  of  the 
equipotential  planes  surrounding  the  wire  is  4  TT  c  where 
c  is  the  strength  of  the  current.  Thus  if  the  strength  c 
were  1^909  we  should  have  24  such  planes ;  if  TT  c  is  not 
a  whole  number,  c  must  be  expressed  in  units  so  small  that 
the  error  involved  in  taking  the  nearest  whole  number 
may  be  neglected.  The  lines  of  magnetic  force  are  circles 
having  their  centres  in  the  axis  of  the  current  and  their 
planes  perpendicular  to  it.  The  intensity  R  of  the  magnetic 


1 8  Electricity  and  Magnetism.         [CHAP.  VI. 


force  at  a  distance  k  from  the  current   is  the   reciprocal 
of  the  distance  between  two  equip otential  surfaces  ;  we  have 

therefore  R  =  —  *° 

k' 

N  §  13.  In  most  telegraphic  instruments  magnets  or  soft 
iron  armatures  are  moved  by  forces  due  to  the  passage  of 
electric  currents  in  certain  wires.  The  apparatus  should  be 
sensitive  so  that  it  may  be  worked  even  by  feeble  currents  ; 
in  designing  the  apparatus  it  should  therefore  be  our  en- 
deavour so  to  arrange  the  wire  conveying  the  current  as  to 
produce  the  most  intense  magnetic  field  which  that  current 
is  capable  of  producing,  and  to  place  the  magnet  or  soft 
iron  acted  upon  in  the  most  intense  part  of  that  field.  By 
so  doing,  and  by  reducing  the  forces  opposing  the  motion 
of  the  soft  iron  or  magnets  as  much  as  possible,  we  render 
the  apparatus  as  sensitive  as  it  can  be  made. 

When  the  magnet  to  be  moved  or  acted  upon  is  large  it 
will  occupy  a  large  portion  of  the  magnetic  field,  and  will 
therefore  experience  a  larger  force  than  if  it  were  small ;  but 
the  force  which  it  experiences  per  unit  of  volume  can  seldom 
if  ever  be  made  so  great  as  when  the  magnet  itself  is  small, 
for  a  small  and  intense  magnetic  field  can  be  produced  with 
a  much  less  current  than  a  large  and  equally  intense  mag- 
netic field.  Hence,  we  find  all  very  sensitive  apparatus 
characterised  by  small  moving  parts.  The  inertia  of  large 
masses  is  also  injurious  in  all  rapidly  moving  parts,  for  not 
only  are  the  large  masses  acted  upon  with  less  force,  but 
owing  to  the  increased  distance  of  the  greater  portion  of 
their  bulk  from  the  axis  on  which  they  must  oscillate  their 
moment  of  inertia  is  increased  even  more  than  their  bulk. 

Similarly,  when  a  wire  conveying  a  current,  or  a  magnet, 
or  a  soft  iron  armature  is  to  move  under  the  influence  of  a 
magnet,  it  must  be  our  aim  so  to  arrange  that  magnet  as  to 
produce  the  most  intense  magnetic  field  possible  at  the 
spot  where  the  moving  piece  is  placed. 

The  mapping  out  of  magnetic  fields   due   to   different 


CHAP.  VI.]  Magnetism.  119 

forms  of  magnet  and  different  arrangements  of  wires  con- 
veying currents  has  therefore  a  great  practical  interest  for 
the  electrician. 

§  14,  The  poles  of  a  magnet  are  not  at  its  extremities,  but 
generally  a  little  way  from  the  end.  It  is  not  necessary  that 
a  magnet  should  be  magnetised  in  the  direction  of  its  length; 
a  bar  may  be  magnetised  transversely  or  indeed  in  any  direc- 
tion. Some  magnets  have  more  than  one  pair  of  poles. 

If  a  long  thin  magnet  be  broken  each  part  becomes  a 
distinct  magnet  having  its  axis  in  the  direction  of  the  old 
axis  ;  from  this  it  appears  that  all  parts  of  the  magnet  are 
in  some  peculiar  polarised  condition,  and  the  actual  poles  of 
any  given  magnet  are  simply  the  result  of  the  combination 
of  all  these  polarised  parts. 

A  piece  of  soft  iron  which  is  a  magnet  by  induction  can 
again  induce  magnetism  in  another  piece  of  soft  iron  :  thus, 
a  magnet  may  sustain  a  long  string  of  nails  each  hanging  to 
its  neighbour.  This  chain  of  nails  has  its  pair  of  poles  near 
the  ends  of  the  first  and  last  nails  in  the  series,  and  affords 
an  example  of  what  is  meant  by  saying  that  all  parts  of  a  mag- 
net are  in  a  polarised  condition ;  each  nail  when  detached 
from  the  series  will  remain  a  magnet  for  some  little  time  in 
virtue  of  its  coercive  force  §  9.  If  a  magnet  be  plunged 
in  iron  filings  and  withdrawn,  these  adhere  most  abundantly 
near  the  poles.  They  stand  out  from  the  magnet  in  tufts, 
largest  where  the  field  of  force  is  strongest,  that  is,  near  the 
poles,  and  the  direction  of  the  chains  or  strings  which  they 
form  corresponds  to  the  direction  of  the  lines  offeree;  each 
separate  filing  becomes  a  small  magnet  for  the  time  being. 

§  15.  Magnets  are  made  from  one  another  by  taking 
advantage  of  this  coercive  force,  which  is  found  to  be  greatest 
in  hard  steel.  A  piece  of  steel  may  be  magnetised  by 
being  stroked  once  or  twice  in  the  same  direction  by  a 
powerful  magnet,  or  even  touched  at  one  end  by  that 
magnet.  Better  results  are  obtained  by  placing  the  two 
opposite  poles  of  equally  strong  magnets  in  the  centre  of 


1 2O  Electricity  and  Magnetism.        [CHAP.  VI. 

the  bar  to  be  magnetised,  and  drawing  them  simultaneously 
away  from  the  centre  to  the  two  ends.  This  operation  is 
repeated  two  or  three  times,  and  the  bar  then  turned  over 
and  treated  in  a  similar  way  on  the  other  face.  The  bar 
magnets  may,  with  advantage,  incline  frc-m  one  another 
while  being  dragged  apart.  A  still  more  complete  magneti- 
sation is  given  by  placing  the  bar  A  B  between  two  powerful 
magnets  N  s  and  N'  s'  as  shown,  and  then  drawing  the  oppo- 

FIG.  61. 


site  poles  of  two  other  magnets  from  the  centre  of  A  B  towards 
the  ends.  There  are  other  methods  of  preparing  magnets 
but  they  all  consist  in  placing  every  part  of  a  bar  of  steel  in 
the  strongest  possible  magnetic  field  and  trusting  to  the  coer- 
cive force  of  the  steel  to  retain  the  induced  magnetism. 

§  16.  The  name  electro-magnet  is  given  to  a  magnet 
formed  of  a  rod  or  bundle  of  rods  of  wrought  iron,  round 
which  an  electric  current  circulates  in  a  coil  of  wire,  as  in 
Fig.  40.  The  electric  current  so  arranged  produces  an 
intense  magnetic  field,  and  the  most  powerful  magnets  are 
produced  in  this  manner.  It  is  found  that  there  is  -a  limit 
to  the  amount  of  magnetism  which  in  this  way  or  any  other 
can  be  induced  in  soft  iron;  when  this  limit  is  approached, 
the  soft  iron  is  said  to  be  saturated  with  magnetism.  Steel 
is  sooner  saturated  than  wrought  iron;  and  as  it  resists  the 
acquisition  of  magnetism  more  than  soft  iron  does,  so  it 
retains  more  of  the  magnetism  it  acquires.  This  resistance 
to  magnetisation  is  also  attributed  to  coercive  force.  Electro- 
magnets can  be  made  of  any  form.  The  two  most  common 


CHAP.  VI.]  Magnetism.  121 

are  the  straight  bar,  in  which  the  poles  are  as  far  apart  as 
possible,  and  the  horse-shoe,  in  which  they  are  brought  close 
together. 

A  piece  of  soft  iron  joining  the  poles  of  a  magnet  is 
called  an  armature;  it  adheres  to  the  poles  and  diminishes 
very  much,  while  in  its  place,  the  intensity  of  the  magnetic 
field  in  the  neighbourhood.  An  electro-magnet  formed  as  a 
complete  ring  produces  no  sensible  magnetic  field  in  its 


FIG.  62. 


Fie.  6* 


neighbourhood ;  nevertheless,  although  without  poles,  it  is 
certainly  a  magnet,  and  produces  many  of  the  magnetic 
phenomena.  A  series  of  equal  magneto  arranged  (as  in 
Fig.  63)  so  that  the  north  pole  of  each  is  in  contact  with 
the  south  pole  of  its  neighbour  will  also  produce  no  magnetic 
field.  An  armature  is  found  to  diminish  sensibly  the  loss 
of  magnetism  which  is  continually  taking  place  in  ordinary 
steel  magnets.  The  armature  is  used  to  suspend  weights 
from  horse-shoe  magnets,  as  in  Fig.  62. 

§  17.  The  strength  m  of  the  poles  of  a  long  soft 
iron  bar  of  one  square  centimetre  section  held  horizon- 
tally in  the  magnetic  field  due  to  the  earth  alone  in  Eng- 
land will  be  equal  to  about  '175  x  32-8  or  574  units, 


122  Electricity  and  Magnetism.         [CHAP.  VI. 

each  pole  would  attract  a  pole  of  opposite  name  with  a 
force/  =  ^y? ,  so  that  if  the  distance  between  the  poles 


were  one  metre,   the  force  exerted  would  be 


ioo 


=  32-9  x  io~4  =  -00329  absolute  units  of  force  equal  to 
the  weight  of  '0000517  grain.  In  order  that  this  should 
be  even  approximately  true  the  prism  must  be  so  long  that 
the  magnetisation  of  the  middle  does  not  interfere  with  that 
of  the  end.  We  should  be  able  to  calculate  the  strength  of 
the  poles  of  any  bar  short  or  long  if  we  were  able  to  find 
the  magnetic  effect  produced  by  a  series  of  equally  magnetised 


elements  in  a  row.  Let  the  black  part  of  each  element 
represent  a  southern  pole  and  the  white  part  a  northern 
pole ;  then  if  each  element  were  so  magnetised  that  the 
black  and  white  parts  were  symmetrical  and  if  the  strength 
of  each  pole  were  a  certain  multiple  of  the  intensity  of  the 
field,  then  «,  would  exactly  cancel  j2 ;  «2  would  cancel  ja, 
and  so  forth,  leaving  s  at  one  end  and  N  at  the  other  at 
the  effective  poles  of  the  magnet ;  but  in  fact  the  action  of 
each  little  element  extends  to  all  the  others,  and  the  sum- 
mation of  all  these  effects  is  so  complex  that  we  must 
abandon  all  attempt  to  calculate  the  strength  of  the  poles 
from  the  intensity  of  magnetisation,  except  in  certain  very 
simple  cases.  The  calculation  given  above  applies  sensibly 
to  all  long  thin  bars  the  cross  section  of  which  is  small 
compared  with  one-twelfth  of  their  length;  thus  our  bar 
of  one  centimetre  cross  section  would  have  to  be  at  least 
five  or  six  metres  long  before  the  formula  would  apply. 

The  magnetic  moment  (§  6)  of  a  long  thin  bar  is,  k  H  s  /, 
where  H  is  the  intensity  of  the  field,  s  the  cross  section  of 


CHAP.  VI.]  Magnetism.  12$ 

the  bar,  /  its  length,  and  k  the  coefficient  of  .magnetic  induc- 
tion ;  the  magnetic  moment  of  a  sphere  in  the  same  field 
will  be 

k  Of     k    6 

ITT^H  — £    .    ..     .     (5)     ^(/(n^vt^*   "~  < 

and  from  this  formula  the  intensity  of  magnetisation  of  a 
given  piece  of  steel  or  other  metal  can  easily  be  calculated 
if  k  be  known,  or  k  may  be  determined  from  actual  obser- 
vation of  the  magnetic  moment. 

§  18.  The  coefficient  k  is  constant  only  for  low  magnetic  in- 
tensities, and  gradually  diminishes  according  to  an  unknown 
law  as  the  maximum  intensity  for  each  material  is  approached. 
The  maximum  intensity  of  magnetisation  for  iron  can  be 
obtained  from  an  experiment  by  Dr.  Joule,  who  found  that 
the  maximum  attraction  he  could  produce  between  an 
electro-magnet  and  its  armature  was  200  Ibs.  per  square  inch 
of  surface.  Calling  this  maximum  attraction  F,  the  intensity 
/,  and  A  the  area  of  the  surfaces  between  which  the  attraction 
is  exerted,  we  have,  when  the  distance  between  the  surfaces 
is  very  small 

F  =   27r^A      ...      (6) 

200  Ibs.  per  square  inch  is  14061  grammes  per  square  centi- 
metre, or  about  13,800,000  absolute  units  of  force  per  square 
centimetre.  Giving  this  value  to  F  in  the  above  equation 
when  A  is  unity,  we  find  for  /  the  value  of  about  1490,  as  the 
maximum  intensity  of  magnetisation  of  which  iron  is  cap- 
able. If  the  value  of  32*8  k  were  constant,  a  magnetic  field 
of  the  intensity  of  about  45  would  be  sufficient  to  magnetise 
iron  to  saturation.  Probably  k  can  only  be  regarded  as 
sensibly  constant  while  the  magnetisation  of  the  iron  is 
below  one  quarter  of  its  maximum  value,  and  from  some 
experiments  by  Miiller  l  we  might  infer  that  the  value  of  k 
near  the  point  of  saturation  is  about  one-third  of  the  value 
given  above,  so  that  a  field  of  magnetic  intensity  equal  to 

1  Pogg.  Ann.  vol.  Ixxix.  1850. 


1 24  Electricity  and  Magnetism.         [CHAP.  VI. 

about  135  would  be  required  to  give  an  electro-magnet 
the  maximum  possible  strength. 

§  19.  The  relative  intensity  of  magnetisation  in  the  same 
•field  for  different  substances  has  not  been  very  fully  studied  ; 
in  other  words,  the  values  of  k  for  different  materials  and 
different  values  of  *  are  not  well  known.  The  following 
table  is  deduced  from  relative  values  obtained  by  Barlow, 
to  which  I  have  added  nickel  and  cobalt,  from  relative 
values  given  by  Pliicker : 

Soft  wrought  iron      .     32-8  Soft  cast  steel     .     23-3 

Cast  iron  .         .         .     23  Hard  cast  steel  .     16*1 

Soft  steel.         .         .     21-6  Nickel       .         .     15-3 

Hard  steel         .         .     17-4  Cobalt        .         .32*8 

These  values  can  only  be  approximately  true.  A  complete 
table  of  the  values  of  k  would  require  to  contain  a  set  of 
values  for  each  material,  and  each  value  of  / ;  whereas  the 
value  of  /  for  which  the  above  values  hold  good  is  not 
known.  The  maximum  intensity  of  magnetisation  for  hard 
steel  is  less  than  for  soft  iron,  and  from  some  experiments 
of  Pliicker,1  it  appears  that  this  difference  is  about  37  per 
cent,  but  a  much  greater  intensity  of  field  is  required  to 
produce  the  maximum  of  magnetisation. 

With  small  values  of  /,  the  value  of  k  for  nickel  was  found 
by  Weber  to  be  five  times  that  of  iron,  but  with  higher  values 
of  i  it  rapidly  became  smaller  than  for  iron,  reaching  a 
maximum  when  i  is  about  30,  increasing  after  this  only  about 
2  per  cent,  when  /  was  doubled. 

§  20.  According  to  experiments  made  by  Pliicker  T 
estimate  the  value  of  k  for  water  at 

—  10-65  x  I0~6- 

The  following  values  of  k  for  different  diamagnetic  sub- 
stances are  calculated  on  this  assumption  from  relative 
values  obtained  by  Pliicker : 

Water      .         .         .         .         .         .      -     10-65   x   lo'8 

Sulphuric  acid  (spec.  grav.  i -839)      .      —      6-8     x   icra 

1  Pogg.  Ann.  vol.  xciv. 


CHAP.  VI.]  Magnetism.  12$ 

Mercury —     33-5     x   IO"6 

Phosphorus —     18-3     x   io~8 

Bismuth —  250        x   io~6 

From  an  observation  by  Weber,  the  value  of  k  for  bismuth 
is  about  —  1 6 -4  x  io-6. 

These  figures  are  given  to  show  very  roughly  the  relative 
value  of  magnetic  and  diamagnetic  action  ;  they  cannot  be 
relied  upon  as  even  approximately  true.  Different  observers 
give  different  relative  values  of  k,  differing  twenty  for  the 
same  substance.  It  must  also  be  remembered  that  they 
are  intended  to  indicate  the  value  of  k  for  equal  volumes, 
not  equal  weights,  of  the  substances. 

§  21.  It  follows  from  equation  (6)  above,  that  the  attrac- 
tion between  a  magnet  and  its  keeper  or  armature  is  propor- 
tional to  the  square  of  the  intensity  of  the  magnetisation,  and 
therefore  in  an  electro-magnet  to  the  square  of  the  current 
multiplied  into  k. 

It  also  follows  that  where  the  intensity  of  magnetisation 
is  the  same  throughout  the  mass  of  iron,  the  attraction  will 
be  simply  proportional  to  the  cross  section  of  the  iron.  The 
object  of  increasing  the  length  of  an  electro-magnet  is  to  get 
a  uniform  field  and  to  place  the  poles  so  that  they  do  not 
interfere  with  one  another. 

By  rounding  or  pointing  the  ends  of  a  magnet,  a  more  in- 
tense magnetisation  is  produced  at  the  ends  than  elsewhere ; 
hence  a  greater  attraction  per  square  centimetre  of  surface. 

The  attraction  between  a  magnet  and  a  keeper  is  directly 
proportional  to  the  intensity  of  the  magnetism  induced  in  the 
keeper,  if  the  keeper  does  not  by  its  mass  or  great  intensity 
of  magnetisation  react  on  the  magnet,  altering  its  intensity. 
The  relative  attraction  of  a  large  magnet  for  small  volumes  of 
different  substances  does  therefore  truly  measure  the  relative 
values  of  k  for  each  substance,  if  the  volumes  are  the  same 
and  the  intensity  of  the  magnetic  field  the  same  throughout 
all  the  volume;  but  these  values  of  k  are  almost  useless 
unless  the  value  of  *  in  absolute  measure  is  also  determined. 


1 26  Electricity  and  Magnetism.       [CHAP.  VII. 


CHAPTER  VII. 

MAGNETIC   MEASUREMENTS. 

§  1.  BEFORE  proceeding  to  study  further  the  laws  of  the 
action  of  currents  upon  currents,  it  is  convenient  to  examine 
the  methods  by  which  the  forces  exerted  by  magnets  one 
upon  another  can  be  definitely  measured  or  expressed  in 
numbers  depending  solely  on  the  centimetre,  gramme,  and 
second  of  time.  To  do  this,  we  require  to  measure 
two  things  only  :  ist,  the  intensity  or  strength,  T,  of 
magnetic  field  which  a  given  magnet  or  arrangement  of 
magnets  produces  at  a  given  point.  2nd,  the  magnetic 
moment,  M  =  m/9  of  the  magnet  which  is  acted  upon  by  the 
assumed  magnetic  field.  Knowing  these  two  quantities,  we 
can,  in  virtue  of  the  laws  already  stated,  calculate  the  couple 
experienced  by  the  magnet  in  the  field.  The  simplest  expe- 
rimental determination  of  the  magnetic  strength  of  a  field 
requires  that  the  field  shall  be  sensibly  uniform  throughout 
the  space  in  which  the  experiment  is  to  be  tried.  The 
magnetic  field  due  to  the  earth  is  sensibly  uniform  within 
the  space  occupied  by  the  experiment,  and  after  giving  a 
general  description  of  the  magnetic  field  due  to  the  earth's 
magnetism,  we  will  proceed  to  examine  how  its  intensity  is 
to  be  measured. 

§  2.  The  direction  of  the  lines  of  force  in  this  field  is  not 
horizontal  except  at  some  places  near  the  equator.  The 
earth  may  be  (very  roughly)  conceived  as  a  large  bar  magnet, 
and  Fig.  58  shows  that  the  lines  of  force  are  parallel  to  the 
axis  of  the  magnet  only  at  points  half-way  between  the 
poles.  The  inclination  of  the  lines  of  force  at  any  place  to 
the  plane  of  the  horizon  is  called  the  dip  or  magnetic  incli- 
nation at  that  place.  If  a  magnet  were  suspended  by  its 
centre  of  figure,  and  were  free  to  assume  any  direction,  it 


CHAP.  VII.]         Magnetic  Measurements.  127 

would  not  remain  horizontal,  but  its  axis  would  lie  in  the 
direction  of  the  lines  of  force ;  in  the  northern  hemisphere 
its  north  pole  would  point  downwards,  and  the  angle  which 
this  axis  makes  with  the  horizontal  plane  is  the  dip  or  in- 
clination. 

The  lines  of  the  earth's  magnetic  force  do  not  usually 
lie  in  planes  running  due  north  and  south.  The  vertical 
plane  in  which  they  lie  at  a  given  place  is  called  the  magnetic 
meridian  of  that  place ;  the  magnet  points  to  the  magnetic 
north.  This  magnetic  north  is  not  any  one  point,  i.e.  the 
magnetic  meridians  at  different  parts  of  the  earth's  surface 
do  not  cut  at  one  point  as  the  true  meridians  do. 

The  geographical  or  true  meridian  of  a  place  is  the  plane 
passing  through  the  place  and  containing  the  true  axis  of 
the  earth.  The  angle  contained  by  the  magnetic  and  true 
meridians  is  called  the  magnetic  declination  at  that  place ; 
the  declination  is  said  to  be  east  if  the  north  pole  of  the 
magnet  points  east  of  the  true  or  geographical  meridian. 
The  declination  is  west  if  the  north  pole  of  the  magnet 
points  west  The  north  and  south  points  of  the  mariner's 
compass  indicate  the  magnetic  meridian. 

§  3.  The  declination  and  dip,  or  inclination,  not  only  vary 
from  place  to  place,  but  also  at  any  one  place  from  hour 
to  hour  and  from  day  to  day.  There  are  some  irregular  varia- 
tions, but  there  are  others  which  are  evidently  periodic. 

1.  There  are  secular  variations,  the   duration  of  which  is 
not  accurately  known.     In   1580,  the  declination  at  Paris 
was  11°  30'  E.  ;  in  1814,  this  had  become  22°  34'  W.,  and 
since  then  the  needle  has  gradually  returned  towards  the  E. ; 
in  1865  the  declination  was  18°  44'  W.     In  certain  parts  of 
the  earth  the  magnetic  and  geographical  or  true  meridians 
coincide  ;  these  points  may  be  joined  by  an  imaginary  line, 
called  the  agonic  line,  or  line  of  no  variation. 

2.  There  are  annual  oscillating  variations  of  declination 
not  exceeding  15'  or  18',  and  varying  at  different  epochs. 

3.  There  are  diurnal  oscillating  variations  of  declination 


128  Electricity  and  Magnetism.       [CHAP.  VI I. 

amounting  at  Paris  on  some  days  to  about  25  ,  on  others 
not  exceeding  5'. 

4.  There  are  accidental  variations  or  perturbations  said 
to  be  due  to  magnetic  storms.  These  variations  occur  with 
great  rapidity,  causing  deflections  to  the  right  and  left,  com- 
parable in  their  rate  or  period  of  alternation  with  ordinary 
telegraphic  signalling ;  accidental  variations  of  70'  have 
been  observed. 

The  dip  also  varies  from  place  to  place ;  it  is  greatest  in 
the  polar  regions,  being  90°  at  the  magnetic  pole.  At  a 
series  of  points  near  the  equator  there  is  no  dip ;  the  line 
joining  these  is  called  the  magnetic  equator.  In  the  southern 
hemisphere  the  direction  of  the  dip  is  reversed,  the  south 
pole  pointing  downwards.  Lines  connecting  places  where 
the  dip  is  equal  are  called  isoclinic  lines. 

§  4.  The  total  intensity  of  the  earth's  magnetism  is  the 
intensity  measured  in  the  direction  of  the  lines  of  force  at 
the  point  where  the  experiment  is  made.     It  is  difficult  to 
make  the  experiment  in  this  way,  especially  as  the  direction 
varies  so  frequently.  The  strength  of  the  horizontal 
component  is  therefore  experimentally  determined, 
and  the  direction  of  the  total  force.  These  two  ele- 
ments give  the  intensity  and  direction  of  the  total 
force ;  for  let  H  (Fig.  65)  be  the  horizontal  com- 
ponent, R  the  total  intensity,  and  0  the  dip,  then 

R  =  ^b    '     •     •     W 

*  §  5.  In  order  to  determine  the  effect  of  any  magnet  upon 
another  or  upon  an  electric  circuit,  its  moment,  M  =  m  /, 
must  be  determined.  Two  experiments  are  sufficient  to 
determine  at  once  the  moment  M  and  the  force  H.  The  first 
of  these  gives  the  value  of  the  product  M  H  by  an  observa- 
tion of  tlie  directing  force  which  the  earth  exerts  on  the 

TVT 

magnet  ]  the  second  gives  the  ratio  -  by  an  observation  of 

H 

the  relative   strength   of  the  magnetic  fields  due   to  the 


CHAP.  VII.]          Magnetic  Measurements.  129 

magnet   and    to  the  earth.      The   following   are    the    two 
experiments  : 

i.  Let  the  magnet  be  hung  so  as  to  oscillate  freely  in  a 
horizontal  plane  round  its  centre  of  figure,  being  directed 
by  the  horizontal  component  of  the  earth's  magnetism.  Let 
the  moment  of  inertia  of  the  magnet  relatively  to  the  axis 
round  which  it  oscillates  be  called  i.1  The  quantity  I  is 
easily  calculable  for  any  regular  figure,  and  can,  moreover, 
be  directly  determined  by  experiment.  Let  the  magnet  now 
be  allowed  to  oscillate  freely,  and  let  the  number  of  com- 
plete or  double  oscillations  per  second  be  n  ;  then 


„  H  = 


O 

In  Rankine's  '  Applied  Mechanics,'  (§  598)  we  have,  equation  (5), 
MJ  =  471"  n  *i  }  where  Mj  is  the  moment  of  the  couple  causing  gyra- 

tion, i^  the  semiamplitude  of  gyration  in  angular  measure.  Let  us  call  F 
\htforce  of  the  couple  due  to  the  magnetic  field  ;  the  arm  of  the  couple 
will  be  z'iL,  where  L  is  the  distance  between  the  poles  ;  hence 
M!  =  z'j  L  F  ;  but  the  moment  of  the  couple  due  to  magnetism  when 
the  magnet  stands  straight  across  the  magnetic  field  is  M  H,  and  the  arm 

of  the  couple  being  then  L,  the  force  must  be  then  and  always  -  =  B' 

orFL  =  M  H;  hence  U-^—i-^  M  H=  4?r  n  **  l  or  M  H  =  4?r  n  I.     Q.  E.  D. 

g  S 

2.  To  obtain  —  ,  fix  N  s  with  its  axis  perpendicular  to 

the  magnetic  meridian,  and  observe  the  deflection  which 
it  causes  on  a  short  magnet  n  s  freely  suspended  so  that 
when  in  the  magnetic  meridian  the  prolongation  of  its  axis 
bisects  N  o  s  (Fig.  66).  The  deflection  dofns  will  depend  on 
the  relative  magnitudes  of  H  and  the  field  produced  by  N  s. 

1  Rankine's  'Applied  Mechanics,'  §  571.  I  have  here  taken  I  as 
equal  to  the  weight  multiplied  into  the  square  of  the  radius  of  gyration, 
following  Professor  Rankine's  example.  Many  writers  define  I  as  equal 
to  the  mass  multiplied  into  the  square  of  the  radius  of  gyration,  and  if 
this  value  of  I  be  used,  the  divisor  g  in  equation  2  must  be  cancelled. 

K 


130 


Electricity  and  Magnetism, 


M 


Let  r  =  o  s  =  o  N  ;  then       =  r3  tan  8 


[CHAP.  VII. 

•     (3) 


Let  m  be  the  strength  of  the  poles  of  the  magnet  N  S;  then  the  foro-! 
which  s  will  exert  at  o  on  a  unit  south  pole  will  be  —   .    .    .in  the 

direction  s  o  ;  the  pole  N  will  exert  an  equal  force  in 
the  direction  o  c.  Let  o  a  and  o  c  represent  these 
forces  in  magnitude  and  direction;  then  b  o  =  T  will 
represent  the  magnitude  and  direction  of  the  lines 
of  force  of  the  magnetic  field  at  o.  We  have  a  o  :  o  b 


:  NS,  orifL 


—  :   T=r:L;orT    = 


meridian  will  be  Mx  T  cos  6 


Let  Mj  be  the  moment  of  the  little  magnet,  the 
couple  due  to  T  tending  to  turn  it  out  of  the  magnetic 

M  ™l  cos  6.     The 

couple   due    to   H    tending  to   bring  it   back   will 
be  Mx  H  sin  9 ;  and  when  one  balances  the  other 

Ml  H  sin  *  =  *L!?i   cosejor-1^  H -?*_';  or* 

r3  H  COS0  H 


=  r3  tan  6.    Q.  E.  D. 
From  equations  (2)  and  (3)  we  have 


H  =  2 


g  r3  tan  0 


and  M  =  2  TT  n     / 


g 


(4) 


(5) 


§  6.  By  means  of  the  single  experiment  last  described  and 
illustrated  by  Fig.  66,  the  moment  M  of  any  permanent  or 
temporary  magnet  can  be  readily  determined  if  H  be  known, 
for  from  equation  (3)  we  have  M  =  rz  H  tan  0  •  H  is 
sufficiently  constant  throughout  England,  and  from  year  to 
year,  to  give  the  value  of  M  with  sufficient  accuracy  for  most 
practical  purposes.  This  method  can  be  used  for  horse-shoe 
magnets  or  magnets  of  any  shape  if  care  be  taken  to  fix  N  s, 
the  line  joining  the  poles  of  this  magnet,  exactly  perpendicular 
to  the  magnetic  meridian  To  do  this,  suspend  the  magnet 


CHAP.  VII.]          Magnetic  Measurements.  131 

by  its  centre  of  figure,  and  let  it  take  up  its  position  on  the 
magnetic  meridian.  Then  noting  this  position  turn  the 

/  magnet  through  exactly  90°  and  fix  it  there. 

(  §  7.  In  order  that  the  values  in  the  above  formulae  should 
be  expressed  in  absolute  measure,  consistent  with  that 
hitherto  adopted,  we  must  be  careful  to  measure  i  in  cen- 
timetres and  grammes.  As  an  example,  the  moment  of 
inertia  of  a  rectangular  prism  of  steel,  two  centimetres  long, 
and  with  a  square  section,  each  side  of  which  measures 
two  millimetres,  and  weighing  1*248  grammes  is 

i  =  1*248  —        1    =  "00416,   •*   0*?\ 
3 

is  the  square  of  the  radius  of  gyration.1 


3 

To  convert  the  value  of  H  found  by  the  above  formulae 
into  grammes,  divide  by  the  value  of  g  in  centimetres 
(981*4  at  Glasgow).  The  mean  horizontal  component  H  in 
England  for  1862  was  0-175  (centimetres,  grammes,  seconds) 
in  absolute  measure.  If  a  free  unit  pole  weighed  one  gramme, 
it  would,  under  the  action  of  the  horizontal  component  of 
the  existing  magnetism  acquire  a  velocity  of  0*175  centi- 
metres at  the  end  of  a  second.  To  convert  this  value  into 
English  absolute  measure  (grains,  feet),  we  must  multiplyit  by 
21-69. 

§  8.  The  value  of  i  for  a  given  magnet  or  other  suspended 
mass  of  simple  form  can  as  above  be  calculated  from 
measurements  of  its  figure  and  its  specific  gravity  or  weight ; 
but  when  the  form  is  complex  and  the  suspended  mass  of 
various  materials,  it  is  better  to  determine  I  experimentally 
by  comparison  with  a  body  of  known  moment  of  inertia. 
To  do  this,  first  observe  the  time  of  one  complete  or  double 
oscillation  /  of  the  magnet  (directed  by  the  earth's  force 
alone),  and  then  add  some  weight  of  simple  form  with  a 
known  moment  of  inertia  i,,  and  observe  the  time  tl  in 
which  the  compound  body  completes  an  oscillation  ;  then,  if 

1  Rankine's  '  Applied  Mechanics,'  §  578. 
K  2 


I32  Electricity  and  Magnetism.        [CHAP.  vil. 

n  be  the  number  of  oscillations  per  second,  /  =  -   and  we 

n1 
have  from  equation  (2) 

or    i    :   i  +  ij  =  /a   :   /,2  ;  whence 

...     (6) 

The  method  by  which  the  value  of  T  [or  the  line  o  b~\  was 
calculated  in  §  5  enables  us  to  determine  the  intensity  of  the 
field  at  any  point  due  to  a  magnet,  so  soon  as  the  moment  M 
and  length  /  are  known.  The  action  of  each  pole  on  a  unit 

pole  at  the  distance  r  will  always  be  equal  to  ^L  =     M2  ; 

and  by  compounding  the  forces  due  to  each  pole  we  obtain 
the  resultant  in  direction  and  intensity. 

The  magnetic  moments  of  two  magnets  of  known  mo- 
ments of  inertia  I  and  ij  can  be  compared  by  means  of  their 
times  of  oscillation  /  and  t\  in  the  same  magnetic  field  ; 
it  follows  from  equation  (2)  that 

M    :   Mt  =  Jj    :    £l_.     .     .     .     (7) 

Similarly,  the  horizontal  intensity  of  two  magnetic  fields 
can  be  compared  by  observing  the  times  /  and  t\  required 
for  a  complete  oscillation  of  any  given  magnet  in  the  two 
•fields  : 

H    :    H,  =  t?    :   t2     .     .     .     (8) 

In  making  this  experiment,  we  must  not  assume  the 
constancy  of  any  given  magnet  even  for  two  successive 
days. 

§  9.  In  calculating  the  effects  of  a  real  magnet,  we  must 
never  forget,  that  although  we  may  experimentally  deter- 
mine the  value  of  m  /,  we  cannot  really  separate  m  from  /, 
because  we  can  never  feel  certain  that  the  length  /  is  equal 


CHAP.  VIII.]     Electro-magnetic  Measurement.  133 

to  the  length  of  the  magnet,  or  to  any  given  fraction  of  it. 
If  the  material  were  uniformly  magnetised,  i.e.  if  it  would 
form  a  number  of  absolutely  equal  magnets  when  cut  up 
into  a  number  of  absolutely  uniform  pieces,  then,  indeed,  the 
length  /  would  be  the  exact  length  of  the  magnet.  In  any 
actual  magnet  the  strength  of  magnetisation  is  found  to  fall 
off  near  the  ends,  and  this  makes  /  shorter  than  the  length 
of  the  magnet ;  moreover,  the  distribution  of  electricity  is 
such  that  the  magnetic  field  produced  by  it  is  different  in 
many  respects,  from  that  which  could  be  produced  by  poles. 


CHAPTER  VIII. 

ELECTRO-MAGNETIC   MEASUREMENT.       ACTION   OF   CURRENTS 
ON    CURRENTS   AND    ON   MAGNETS. 

§  1,  THE  series  of  units  described  in  Chapter  V.  would 
suffice  for  all  electrical  purposes,  but  they  are  not  very  well 
adapted  for  the  calculation  of  the  effect  of  electric  currents 
upon  one  another,  or  upon  magnets. 

We  obtained  the  set  of  electrostatic  units  from  a  series  of 
equations  which  did  not  involve  the  forces  acting  between 
currents  and  magnets ;  starting  from  the  measurement  of 
these  latter  forces,  we  obtain  a  distinct  system  of  units, 
which  will  be  termed  electro-magnetic  units,  from  a  series  of 
equations  which  do  not  involve  the  forces  of  electrostatic 
repulsion  and  attraction.  Electro-magnetic  units  are  more 
commonly  used  in  telegraphy  than  electrostatic  units.  In 
Chapter  VI.  §  1 2  a  definition  of  the  unit  current  was  sug- 
gested, depending  on  the  force  with  which  a  current  acts  on 
a  magnetic  pole.  According  to  this  definition,  the  unit 
curicnt  is  such  that  every  centimetre  of  its  length  acts  with 
unit  force  on  a  unit  magnetic  pole  at  a  distance  of  one  cen- 
timetre from  all  parts  of  the  current.  To  obtain  this  last 


134  Electricity  and  Magnetism.      [CHAP.  VI  1  1. 

condition  the  wire  conveying  the  current  must  be  bent  in  a 
circle,  at  the  centre  of  which  hangs  the  free  magnetic  pole. 
The  force  (/)  exerted  on  the  pole  of  a  magnet  in  its 
neighbourhood  is  proportional  to  the  magnetic  strength  (m) 
of  -the  pole  of  the  magnet,  and  to  the  strength  of  the  cur- 
rent c  ;  and  if  the  conductor  be  at  all  points  equi-distant 
from  the  pole,  the  force  is  proportional  to  the  length 
of  the  conductor  L.  It  is  also  inversely  proportional  to 
the  square  of  the  distance  k  of  the  pole  from  the  conductor, 
and  is  affected  by  no  other  circumstances.  Hence  we  have 

/=  ...     (D 


from  which  c  =  i  —  ,  giving    the    definition   of  the  unit 

current  stated  above. 

§  2.  Let  us  use  the  capital  letters  Q,  I,  R,  c,  and  s  to 
indicate  the  quantities  in  electro-magnetic  measure  which 
were  indicated  by  ^,  /,  r,  c,  and  s  in  electrostatic  measure; 
then,  taking  the  unit  of  current  as  determined  by  the 
equation  in  §  i,  we  have,  from  the  equations  Q  =  c  t, 

i  =  —  ,  R  =     —  ,  and  s  =  —  ,    a  complete  new  series  of 

units  bearing  a  definite  ratio  to  the  electrostatic  units  ;  by 
experiment  it  has  been  found  that  c  =  28,800,000,000  c. 
This  numerical  coefficient  will  be  termed  v. 


c=  - 


Q  = 


_  q 


I   =  V 


s  = 


V 

The  above  series  of  equations  express  the  relations  be- 
tween the  numbers  expressing  electrical  magnitudes  in  the  two 
series  of  units  ;  they  all  follow  directly  from  the  fundamental 
equations.  The  relations  of  the  electro-magnetic  units  to 
one  another,  and  to  the  mechanical  units  may  be  summed 
up  as  follows  :  The  unit  current  conveys  a  unit  quantity  of 
electricity  per  second  across  any  section  of  the  circuit.  The 
unit  current  will  be  produced  in  a  circuit  of  unit  resistance 


CHAP.  VIII.]     Electro-magnetic  Measurement.  135 

by  the  unit  electromotive  force.  The  unit  current  in  a  con- 
ductor of  unit  resistance  produces  an  effect  equivalent  to  the 
unit  of  work  per  second.  Lastly,  the  unit  current  flowing 
through  a  conductor  of  unit  length  will  exert  the  unit  force  on 
a  unit  pole  at  a  distance  of  one  centimetre.  It  is  this  last 
condition  which  is  peculiar  to  the  electro-magnetic  series. 

§  3.  Let  a  very  short  magnet  n  ^(Fig.  67),  say  \  inch  in  length, 
be  freely  hung  at  the  centre  of  a  circular 
coil  A,  of  considerable  relative  diameter, 
say  1 8  inches,  and  let  the  plane  of  the 
coil  be  placed  in  the  magnetic  meridian, 
then  the  value  c  in  electro-magnetic 
measure  of  any  current  passing  through 
the  coil  and  deflecting  the  magnet 
through  the  angle  0,  is  given  by  the  fol- 
lowing expression : 

c  =    H/'2    tan  0     ...     (2) 

L 

where  H  is  the  horizontal  component  of  the  earth's  magnetism 
and  L  is  the  length  of  the  wire  forming  the  coil.  All  dimen- 
sions must  be  in  centimetres  if  H  is  measured  in  the  units 
already  adopted. 

From  this  equation  we  see  that  the  current  will  be  pro- 
portional to  the  tangent  of  the  angle  of  deflection,  and  a 
galvanometer  of  this  construction  is  therefore  called  a  tangent 
galvanometer  ;  moreover,  knowing  the  value  of  H,  we  shall, 
with  tangent  galvanometer,  be  able  directly  to  measure 
currents  in  absolute  measure,  independently  of  any  know- 
ledge of  the  magnetic  moment  of  the  needle  employed,  and 
independently  also  of  any  peculiarity  in  the  instrument  used. 
A  current  so  measured  in  Australia  is  therefore  at  once  com- 
parable with  a  current  measured  in  England. 

The  resultant  electro-magnetic  force  (/)  exerted  at  the  centre  of  a 
circular  coil  of  radius  k,  by  the  current  C,  will  by  equation  I  be/*  =  — : 

the  two  poles  of  a  short  magnet  hung  in  the  centre,  with  its  magnetic 
axis  in  the  plane  of  the  circular  coil,  will  experience  equal  and  opposite 


136 


Electricity  and  Magnetism.      [CHAP.  vm. 


forces,  each  equal  to  f  m,  where  m  is  the  strength  of  each  pole  of  the 
magnet.  If  /  be  the  distance  separating  these  poles  or  forces  (equal 
sensibly  to  the  length  of  the  magnet),  then  the  magnet  experiences  what 

is  termed  a  couple,  the  moment  of  which  \?,fm  I  = . 


Let  N  s 


a  c  L  m  I 
is  now  cos  6  — — - _ . 


be  the  plan  of  the  magnet  (Fig. 
68)  as  it  hangs  in  the  plane  of 
the  coil  of  wire,  and  let  Nx  s,, 
making  an  angle  0  with  N  S,  be 
any  new  position  which  it  takes 
up  under  the  influence  of  the 
current.  Then,  supposing  the 
magnet  to  be  small  compared 
with  the  diameter  of  the  coil, 
the  poles  remain  sensibly  at  the 
centre  ;  the  force  f  remains  the 
same,  but  the  perpendicular  dis- 
tance N!  C  between  the  poles  on 
which  the  equal  and  opposite 
forces  are  exerted  is  now  equal 
to  /  cos  9,  and  hence  the  couple 

This  couple  is  opposed  by  the  directing  couple 


due  to  the  earth's  magnetism.  Let  us  call  H  the  horizontal  component 
of  the  earth's  magnetism  at  the  place  in  question  ;  then  the  force  due 
to  its  action  on  each  pole  will  be  H  m ;  the  perpendicular  distance  sx  c 
separating  the  two  parallel  forces  will  be  /  sin  6,  and  whole  couple  will 
therefore  be  sin  0  H  m  I ;  and  when  the  magnet  is  in  equilibrium,  under 
the  combined  forces  of  the  directing  current  and  the  earth's  magnetism, 
we  have 


cos  6     __    =  sin  6  H  m  I ;  whence 


1 


sin  0 
cos  6 


•     K    =  tan  6 


§  4.  All  the  relations  between  force  and  currents  of  a  given  form  and 
strength  may  be  deduced  mathematically  from  the  following  theory, 
due  to  Ampere.  I.  The  force  with  which  two  small  lengths  or  elements 
of  currents  act  upon  each  other  is  in  the  direction  of  the  line  joining  the 
centres  of  these  elements,  and  this  force  is  inversely  proportional  to  the 
square  of  the  distance  between  the  elements. 

2.  Let  there  be  two  short  wires  m  n  and  m^  n±  (Fig.  69),  parallel  to  one 


CHAP.  vill.  ]     Electro -magnetic  Measurement. 


137 


another,  and  perpendicular  to  the  line  d  joining  their  centres.     Let 
the  current  c  flow  through  m  n,  and  ^  through  m}  nl ;  then  the  force 
with  which  these  two  little  elements  of  currents  attract  one  another  if 
flowing  in  the  same  direction  or  repel                        FIG.  69. 
one  another  if  going  in  opposite  direc-      I    i & j  *  I 


tions  is 


3.  If  the  two  short  wires  be  placed  as  in  Fig.  69^,  so  as  to  lie  in  the 
direction  of  the  line  d  joining  their  centres,  the  force  acting  between 
them  is  half  the  above :  it  is  a  repulsion  if 

the  currents  flow  in  the  same  direction,  an                     FIG.  6ga. 
attraction  if  they  flow  in  opposite  directions.      — --- — • 

4.  If  the  two  short  wires  be  placed  so  as  to 

be  both  perpendicular  to  the  line  d,  but  so  that  m  n  is  also  perpendicular  to 
77/1 7z,,  as  in  Fig.  69/7,  then  the  currents  neither  attract  nor  repel  one  another. 

5.  If  one  element  lies  along  d,  and  the  other  is  perpendicular  to  it, 
the  currents  neither  attract  nor  repel  one  another. 

6.  Let  A  B  (Fig.  6gc)  be  any  short  wire  con- 
veying any  current  c  in  any  direction  relatively     ™ 
to  the  short  wire  A,  B,,   conveying  another     • 
current  c^     Let  the  line  d  join  the  centres  of 

A  B  and  A!  Bj  ;  draw  the  line  xl  in  the  direction  of  d  and  draw^  per- 
pendicular to  #!,  and  of  such  magnitude  that  the  resultant  of  two  forces 
y\  and  xl  would  be  equal  to  the  current  clt  and  lie  in  the  direction 
A!  BJ.  On  a  similar  plan  draw  y  parallel  to  ylt  and  draw  x  and  z, 
rectangular  components  such  that  if  y,  x,  and  z  were  forces,  their  re- 

FIG.  6gc. 


FlG.  69(j. 


A  i 


sultant  would  be  equal  to  c,  and  lie  in  the  direction  A  B.  Then 
the  resultant  action  of  the  current  in  A  B  on  the  current  in  AJ  B1?  will 
be  the  sum  of  that  of  the  three  currents  jr,  x,  and  z  on  the  two  currents 
y^  and  x^.  We  may  observe  that  this  reduces  itself  to  the  sum  of  the 
action  of  x  on  xlt  which  we  can  calculate  from  3.  above  added  to  the 
action  of  y  on  ylt  which  we  can  calculate  from  2.  above  :  for  z  is 
inoperative  on  y^  y  does  not  attract  or  repel  xlt  nor  does  yl  attract 


138  Electricity  and  Magnetism.      [CHAP.  VIII. 

or  repel  x.  In  dealing  with  wires  of  any  considerable  length,  the 
action  of  each  little  element  of  one  wire  on  all  the  elements  of  the  other 
must  be  taken  into  account,  and  the  results  summed.  This  summation 
or  integration  gives  the  results  detailed  in  the  following  paragraphs  ; 
and  these  results,  being  confirmed  by  experiments  on  closed  circuits, 
establish  the  truth  of  the  theory  as  applied  to  closed  circuits. 

It  follows  from  the  above  theory,  that  the  action  of  a  small  closed  circuit 
at  a  distance  is  the  same  as  that  of  a  small  magnet  having  its  axis  placed 
perpendicularly  to  the  plane  of  the  current,  and  having  a  moment  equal 
to  the  product  of  the  current  into  the  area  encompassed  by  the  circuit  ; 
thus,  if  the  circuit  be  circular,  the  moment  of  the  magnet  will  be  C  IT  &. 
Let  two  small  circles,  with  radii  k  and  kly  be  placed  at  a  great  distance 
D  from  one  another,  in  such  a  manner  that  their  planes  are  at  right 
angles  to  each  other  and  that  the  line  D  is  in  the  intersection  of  the 
planes.  Let  an  equal  current  C  circulate  in  each  of  these  conductors  ; 
forces  will  act  between  them,  tending  to  make  their  planes  parallel  and 
the  direction  of  the  currents  opposite  ;  these  forces  will  produce  a 
couple,  of  which  the  moment  will  be 


If  now,  M,  D3,  TT  /£2,  if  k-?  be  all  made  unity,  this  will  give  a  value  for  the 
unit  of  current  C,  which  will  be  the  same  as  that  founded  on  the  action 
between  a  current  and  a  magnet.  It  also  follows  that  the  unit  current 
enclosing  a  circle  of  unit  area  will  produce  the  same  couple  on  a  magnet 
at  a  distance  as  would  be  produced  by  a  small  magnet  of  unit  moment. 

§  5.  We  found  one  means  of  measuring  the  strength  of  a 
current  by  comparing  the  magnetic  field  it  produced  with 
the  horizontal  component  of  the  earth's  magnetism  H.  We 
may  determine  or  measure  the  strength  of  a  current  in  the 
same  units  by  measuring  the  action  between  different  parts 
of  the  current  itself  as  determined  by  Ampere's  theory. 

Let  a  coil  of  wire  A  be  hung  inside  a  larger  coilB  (Fig.  70), 
and  so  directed  by  means  of  its  suspension  that,  when  no  cur- 
rents pass  through  the  two  coils,  the  plane  of  A  is  perpendicu- 
lar to  that  of  B.  When  one  and  the  same  current  is  allowed 
to  flow  simultaneously  through  A  and  B,  they  experience  a 
deviating  couple  proportional  to  c2,  and  depending  for  its 
absolute  value  on  the  value  of  the  diameters  k  and  k\  of 
A  and  B,  and  on  the  number  of  turns  v  and  v\  in  these 


CHAP.  VIII.]     Electro-magnetic  Measurement.  139 

coils.     If  the  plane  of  the  coil  B  be  so  turned  that,  when 
the  current  is  passing,  the  plane  of  A  lies  in  the  magnetic 
meridian,  then  the  only  couple  tend- 
ing to  bring  A  back  into  its  original 
position  will  be  that  due  to  its  sus- 
pension.    Then  calling  the  deflec- 
tion or  angle  between  the  planes 
of  the  coils  0,  expressed  in  circular 
measure,  we  have 


c  =  ,*  , 

~  COS 

where  a  is  a  constant,  varying  in 
different  instruments,  but  which  for 
any  one  instrument  can  be  found  experimentally  or  deter- 
mined once  for  all  by  the  maker.  This  method  was  first 
employed  by  Weber,  and  the  instrument  is  called  Weber's 
Electro-Dynamometer. 

Let  us  call  the  directing  couple  G  and  the  deviating  couple  M.  When 
the  coil  A  is  in  equilibrium,  M  =  G.  The  value  of  G  depends  on  the 
mode  of  suspension  ;  if  it  be  by  a  single  wire,  the  torsion  varies  simply 
as  the  angle  of  deflection  6,  or 

G  =  /*  e    .    .    .    (5) 

•where  u  stands  for  the  expression 


g  g?        '-/« 

in  which  the  several  letters  have  the  same  meaning  as  in  Chapter  VII. 
§  8  ;  I  being  now  the  moment  of  inertia  of  the  suspended  coil  instead  of 
the  suspended  magnet,  and  ij  the  moment  of  inertia  of  a  mass  of  simple 
form  added  to  determine  experimentally  the  value  of  I. 
The  value  of  the  deflecting  couple  is  given  by  the  equation 
M  =  £  c2  cos  e     .     .     .     (7) 

in  which  0  is  a  constant  determined  by  Ampere's  theory.  Let  k  be  the 
radius  of  the  large  coil  B,  k^  the  radius  of  the  small  coil  A.  Let  k^  be 
the  distance  from  the  centre  of  coil  A  to  the  periphery  of  coil  B  ;  k^  =  k 
when  the  coils  have  a  common  vertical  axis  ;  let  V  be  the  number  of  turns 
of  v/ire  in  the  large  coil ;  v  the  number  of  turns  in  the  small  coil,  then 


140  Electricity  and  Magnetism.      [CHAP.  VIII. 

Since  M  =  G  from  equations  (7)  and  (5)  \ve  have 
c  = 


£     e 


u    cos  0 


(9) 


The  values  of  £  and  p  are  evidently  constant  for  any  one  instrument. 

If  the  suspension  is  bifilar,  equations  (5)  and  (6)  must  be  modified  : 
we  then  have 

G  =  u  sin  9     .     .     .     (10) 
and 

4  f2  ii 

//      —  •  •* 


(ii) 


where  w^  is  the  weight  of  the  added  mass  and  w  the  weight  of  the 
coil  A. 

Then  from  equations  (10)  and  (7)  we  have 


c=y,' 

for  both  cases,  where  6  is  small, 


(12) 


6  being  in  circular  measure. 

§  6.  The  following  is  another  method,  due  to  F.  Kohl- 
rausch,  of  measuring  currents  in  absolute  measure  by  means 
of  a  tangent  galvanometer  and  a  single  coil  suspended  by 
two  wires. 

FIG.  71. 


Let  a  coil  A  (Fig.  71)  of  k  radius  and  n  turns  be  hung  by  a 
bifilar  suspension,  with  its  plane  perpendicular  to  the  plane 


CHAP.  VIII.]      Electro-magnetic  Measurement.  141 

of  the  magnetic  meridian.  Observe  the  deflection  0  pro- 
duced in  this  coil  by  the  current  c  and  the  simultaneous 
deflection  flj  produced  by  the  same  current  on  the  needle 
of  a  tangent  galvanometer  B  of  radius  £1?  then 

c  = 


The  coil  A,  when  the  current  C  flows  through  it,  is  equivalent  to  a 
magnet  of  the  moment  C  n  TT  k-  ;  and  calling  H  the  horizontal  com- 
ponent of  the  earth's  magnetism,  the  couple  experienced  by  the  coil 
when  deflected  through  the  angle  6  will  be  H  C  n  IT  kz  cos  0.  The 
directing  couple  due  to  the  bifilar  suspension  is  n  sin  0.  Hence,  when 
the  one  balances  the  other, 

H  c  n  TT  k2  cos  &  =  n  sin  9 

and  C  =  -  ^  —  —  tan  0     ...     (14) 
H  .  n  TT  K1 

The  value  oi  fj.  can  be  found  as  by  the  last  section.  From  this 
equation  alone  we  might  find  c  in  terms  of  H  ;  but  we  have  also, 
calling  0X  the  deflection  produced  by  the  same  current  C  passing  through 
the  tangent  galvanometer  of  radius  k-^ 


tan 


L 

hence,  eliminating  H,  we  have  equation  (  14)  as  given  above  (eliminating 
C,  we  might  find  H  from  the  same  equations).  It  should  be  observed 
that  n  IT  kz  is  more  strictly  the  sum  of  the  areas  enclosed  by  the  turns 
of  different  diameter  of  which  the  coil  is  composed. 

§  7.  Let  a  current  traverse  two  wires  in  succession,  each 
bent  so  as  to  enclose  a  circle  of  the  radius  k.  Let  these 
wires  be  hung  in  parallel  planes  at  the  distance  a,  with  their 
centres  in  the  same  axis.  Then,  if  the  current  be  sent 
round  the  wires  in  the  same  direction,  they  will  attract  one 
another;  if  in  the  opposite  direction,  they  will  repel  one 
another  with  a  force 


If  two  coils,  each  containing  n  turns,  be  thus  hung,  the 
force  with  which  they  attract  or  repel  each  other  will  be 

F,  =  4  TT  «2  c2  £    .     .     .     (16) 


142 


Electricity  and  Magnetism.      [CHAP.  VI II. 


FIG.  72. 


hence,  knowing  the  current,  we  can  determine  the  force,  or, 
weighing  the  force,  can  measure  the  current. 

By  placing  two  fixed  parallel  coils,  A  and  B,  opposite  each 
other,  as  in  Fig.  72,  and  passing  a  current  round  them  in 

opposite  directions,  we 
obtain  a  sensibly  uni- 
form field  of  magnetic 
force  between  the  flat 
coils.  If  a  third  flat  coil  D 
be  hung  between  them  it 
will  be  attracted  by  one 
and  repelled  by  the  other, 
and  a  good  electro-dy- 
namometer may  be  con- 
structed on  this  principle. 
The  actual  value  of  the 
current  corresponding  to  a  given  couple  experienced  by  the 
suspending  wires  e  and/,  indicated  by  the  torsion  of  a  wire, 
is  experimentally  determined  once  for  all  by  comparison  with 
a  standard  instrument.  A  second  suspended  flat  coil  D1  is 
required  to  make  the  system  independent  of  the  earth's 
magnetism,  and  this  coil  DJ  may  advantageously  be  placed 
between  two  more  fixed  flat  coils 
arranged  so  as  to  double  the  couple 
experienced  by  the  suspended  system. 

§  8.  The  intensity  of  the  magnetic  field 
produced  by  a  circle  at  any  point  B  on  an  axis 
perpendicular  to  the  plane  of  the  circle  is 
given  by  the  following  formula  : 

Let  A  C  (Fig.  73),  the  radius  of  the  circular 
conductor,  be  =  k.  Let  C  =  the  current. 
Let  A  B  =  x.  Let  F  =  the  intensity  of 
the  field. 

*  c  k  ' 


Fie.  73. 


ThenF   = 

(&  +  a3)! 
At  A,  the  centre  of  the  coil,  the  intensity  is 


(17) 


CHAP.  VIII.]     Electro-magnetic  Measurement.  143 

Let  an  insulated  wire  be  wound  round  a  cylinder  of  the  length  2  /, 
forming  a  spiral.     JLet  the  distance  of  the  point  M  (Fig.  74)  from  the 

FIG.  74. 


nearest  end  of  the  cylinder  =  M  o  =  a.  If  the  point  were  inside  the 
spiral,  a  would  be  affected  with  the  negative  sign. 

Let  the  line  joining  an  element  of  a  spiral  with  M  =  e. 

Let  the  number  of  turns  be  n,  then  the  intensity  of  the  magnetic  field 
at  M  is 

T  =   Cir  n      (  a  +  2/  —        °L.  _  \ 

I          \  y  &  +  (a  +  2  I)*  V  &  +  a?' 

Let  the  angle  A  M  O  =»  ^,  and  the  angle  B  M  o  =  rj/j ;  then 
T  =  !^1!!  (cos  *  -  ^). 

This  applies  to  inside  as  well  as  outside,  remembering  that  cos  y± 
will  be  negative  inside  the  spiral,  so  that  we  have  virtually  cos  ^ 
+  cos  if^. 

The  force  is  at  a  maximum  in  the  centre. 

Call  the  diagonal  of  the  spiral  2  d ;  then  the  intensity  of  the  magnetic 
field  at  the  centre  will  be 

2  c  TT  n 
FW=    _._. 

If  the  length  of  the  spiral  be  40  times  its  diameter,  the  intensity  of 
the  magnetic  field  does  not  vary  by  one  per  cent,  throughout  |-  of  its 
length,  and  not  'I  per  cent,  throughout  y~  of  its  length. 

§  9.  A  long  spiral  of  insulated  wire  of  small  diameter 
relatively  to  its  length  is  commonly  called  a  solenoid, 
although,  strictly  speaking,  this  name  applies  only  to  a  series 
of  perfectly  parallel  and  equal  rings  all  perpendicular  to  a 
common  axis  and  in  all  of  which  an  equal  current  is  flow- 
ing. The  material  representation  of  the  solenoid  differs 
experimentally  little  from  its  hypothetical  type.  We  have 
seen  that  a  current  flowing  round  a  circle  or  a  series  of 


144  Electricity  and  Magnetism.      [CHAP.  VIIL 

circles  in  one  plane  acted  upon  a  magnetic  pole  or  upon  an 
electric  current  at  a  distance  as  if  it  were  a  short  magnet  of 
the  moment  c  n  ?r  >£'2,  where  n  is  the  number  of  turns. 

If  a  solenoid  beginning  at  A  were  very  far  prolonged 
towards  B,  it  would  act  on  all  points 
within  a  finite  distance  of  A,  as  if  at  A 


there  was  a  magnetic  pole  of  the  strength 
c  ;/  TT  >£2,  in  which  n  is  the  number  of 
turns  in  the  solenoid  per  centimetre. 

An  actual  solenoid  acts  as  if  two  such  endless  solenoids 
were  superposed,  having  the  same  current  flowing  through 
them  in  opposite  directions  ;  one  beginning  at  A  and  the 
other  at  B.  Then  we  should  have  one  north  pole,  say  at  A, 
and  one  south  pole  at  B,  and  all  the  rest  of  the  turns 
cancel  one  another;  hence  the  magnetic  moment  of 
the  solenoid  is  c  n  ?r  /£2  L,  where  L  is  its  length. 

If  keeping  the  actual  number  of  turns  constant  we 
shorten  the  length  L,  we  increase  n  just  as  we  diminish  L, 
so  that  the  moment  does  not  vary. 

Imagine  a  watch  hung  in  a  solenoid  in  such  a  position 
that  the  current  circulates  with  the  hands  of  the  watch. 
Then  the  south  'pole  will  be  at  the  end  towards  which  the 
face  of  the  watch  is  turned. 

§  10.  If  a  magnet  be  hung  with  its  north  pole  downwards 
over  the  centre  of  a  vertical  solenoid  in  which  the  current 
is  circulating  in  the  direction  of  the  hands  of  a  watch 
(looking  at  spiral  and  watch  from  above),  then  the  north 
pole  will  be  attracted  when  outside  the  solenoid,  as  if  by 
a  south  pole  ;  it  will  continue  to  be  sucked  into  the  solenoid, 
even  after  entering  in  it,  although  the  force  with  which  it 
is  pulled  down  will  diminish.  The  south  pole  of  the 
magnet  is  repelled  upwards,  but  with  less  force  than  the 
north  pole  is  sucked  downwards.  When  the  centre  of  the 
magnet  has  reached  the  centre  of  the  solenoid,  the  magnet 
will  be  in  equilibrium  so  far  as  magnetic  forces  are  con- 
cerned ;  if  allowed  to  fall  further,  the  magnetic  forces  will 


CHAP.  VIII.]     Electro-magnetic  Measurement.  145 

resist  the  motion,  and  if  the  current  be  powerful  enough, 
these  forces  will  carry  the  weight  of  the  magnet  and  prevent 
it  from  falling  further. 

Feilitsch  made  the  following  experiment,  showing  how 
the  force  diminishes,  .  using  a  magnet  io'i  centimetres 
long,  2*03  centimetres  diameter,  weighing  23*678  grammes, 
and  a  spiral  or  solenoid  of  126  turns,  29-5  centimetres  long, 
and  i2'9  centimetres  internal  circumference.  The  following 
table  gives  the  distances  a  of  the  centre  of  the  magnet  from 
the  centre  of  the  spiral,  and  g  the  force  in  milligrammes  : 


a.    18-7  |  167  j  14-7 
g.    190   j  382    |  493 


127  I  107  [     87  I  67 
474  I  313  I  "5    132 


47  I  27     -07  |  --i 


16      ii        2    I  -  i 


The  poles  of  the  magnet  when  in  equilibrium  inside  the 
solenoid  are  placed  relatively  to  the  spiral,  as  if  the  spiral 
had  magnetised  a  piece  of  soft  iron  of  the  same  length.  Soft 
iron  is  therefore  drawn  in  just  as  the  magnet  would  be,  and 
the  north  pole  of  the  soft  iron  corresponds  to  the  north  pole 
of  the  solenoid. 

§  11.  A  hollow  magnet  does  not  in  this  respect  resemble 
a  solenoid. 

If  the  north  pole  of  a  magnet  A  were  introduced  into  the 
interior  of  a  hollow  magnet  B  at  its  south  pole,  A  would  be 
repelled  from  B  after  it  had  penetrated  to  a  very  short 
distance  ;  and  if  a  rod  of  soft  iron  was  placed  inside  a  hollow 
steel  magnet,  the  north  pole  of  the  magnet  would  induce  a 
south  pole  in  the  end  of  the  iron  next  it. 

This  experiment  proves  conclusively  that  we  cannot  re- 
gard a  magnet  as  simply  produced  by  a  series  of  currents 
circulating  round  its  exterior  periphery ;  but  FlG  ?6> 

it    agrees  with   the  hypothesis    that   the  O  (P 

magnet  consists  of  an  immense  number  of       O  "fc 

little  solenoids  lying  side  by  side.    In  fact,      O 
conceive  a  number  of  such  solenoids,  side     C3 
by  side,  the  end  views  of  which  are  shown,       ^/^  r^  O>^ 
as  in  Fig.  76,  with  the  current  flowing  in  ^*  >B     * 

the  direction  shown  by  the  arrows,  then  all  the  elements  of 

L 


146 


Electricity  and  Magnetism.      [CHAP.  VIIL 


each  little  circuit  inside  the  ring  would  move  in  the  direc- 
tion followed  by  the  hands  of  a  watch ;  all  the  elements 
outside  would  move  in  the  opposite  direction.  On  a  point 
at  y  the  former  would  be  most  powerful ;  on  a  point  at  .r, 
the  latter;  the  radial  currents  counteract  one  another,  for 
there  are  as  many  in  one  direction  as  in  the  other. 

§  12.  For  general  purposes,  we  may  regard  a  solenoid  as 
equivalent  to  a  magnet,  so  far  as  regards  all  points  outside 
of  the  cylinder;  the  effect  of  introducing  soft  iron  into  the 
interior  of  the  cylinder  is  to  make  the  field  of  force  outside 
the  cylinder,  more  intense.  It  may  thus  become  as  much  as 
about  32-8  times  more  intense  than  before.  The  direction 
of  the  lines  of  force  is  very  little  altered.  Fig.  77  shows 

FIG.  77. 


roughly  the  field  of  force  due  to  a  solenoid,  Fig.  78,  the  field 
of  force  after  a  soft  iron  wire  has  been  introduced.  The  soft 
iron  wire  concentrates  the  lines  of  force  near  the  poles, 
and  thus  over  a  limited  space  enables  the  current  passing 
through  the  solenoid  to  produce  very  powerful  effects ;  its 
action  in  this  respect  is  somewhat  analogous  to  that  of  a 
lens  used  to  concentrate  light  on  a  spot  where  illuminating 
action  is  required. 


CHAP.  IX.l          Electro-magnetic  Induction.  147 


CHAPTER   IX. 

MEASUREMENT   OF   ELECTRO-MAGNETIC    INDUCTION. 

§  1.  A  DESCRIPTION  of  the  principal  phenomena  of  magnetic 
induction  has  already  been  given,  and  we  will  now  con- 
sider how  to  estimate  numerically  the  effects  produced 
under  various  circumstances. 

Electro  magnetic  force. — When  the  intensity  of  a  given  mag- 
netic field  produced  by  a  magnet  or  by  electrical  currents, 
has  been  determined,  the  induced  current  produced  in  a  con- 
ductor moving  in  that  field  is  easily  determined.  Every  part 
of  the  conductor  moving  in  a  field  and  conveying  a  current 
(induced  or  not)  is  acted  upon  by  a  force  perpendicular  to 
the  plane  passing  through  its  own  direction  and  the  lines  of 
magnetic  force  in  the  field.  This  force  is  equal  to  the 
product  of  the  length  of  the  conductor  into  the  strength  of 
the  current  in  electro-magnetic  measure,  the  intensity  of  the 
magnetic  field,  and  the  sine  of  the  angle  FIG 

between  the  lines  offeree  and  the  direc- 
tion of  the  current.  Thus,  if  A  B  (Fig. 
79)  be  the  element  of  the  conductor, 
and  the  lines  of  force  be  in  the  plane 
of  the  paper  as  dotted,  then  the  direc- 
tion of  the  force  due  to  the  field  and 
current  is  perpendicular  to  the  plane  of 
the  paper.  Let  the  intensity  of  the  magnetic  field  =  T, 
the  strength  of  the  current  in  A  B  =  c,  the  angle  A  B  c  =  a, 
and/=  the  force. 

Then          /=TC  x  ABsina     .     .     .     (i) 
The  force  is  exactly  the  same  as  if  the  conductor,  instead 
of  being  of  the  length  and  in  the  direction  A  B,  were  really 
of  the  length  and  in  the  direction  A  c.     Let  A  B  (Fig.  80) 

L  2 


148  Electricity  and  Magnetism.         [CHAP.  IX. 

represent  a  piece  of  the  conductor  in  which  a  current  c  is 

flowing  from  A  to  B.     Let  D  o 
be  the  direction  of  the  lines  of 
magnetic  force  so  that  a  mag- 
net N  s  would  place  itself  in  the 
field   as  shown  in   the  figure. 
The  force /experienced  by  the 
conductor  will  tend  to  lift  it 
perpendicularly  to   the   plane 
AOD.     Let   FO    represent  in 
magnitude  and  direction    the 
current  c  and  D  o  the  magni- 
tude and  direction  of  the  intensity  of  the  magnetic  field, 
then  /  per  unit  of  length  =  T  c  sin  a,  but  c  sin  a  =  the 
perpendicular  distance  from  E  F  to  o  D  and  T  =*  D  o ;  hence 
the  area  of  the  parallelogram  E  F  o  D  =  /  per  unit  of  length. 
A  current  flowing  from  west  to  east  is  lifted  by  the  earth's 
magnetism.     The  following  is  a  rule  by  which  to  remember 
which  way  the  magnetism  of  any  field  would  impel  any  cur- 
rent.   Place  a  corkscrew  perpendicular  to  the  plane  E  F  o  D 
and  turn  it,  as  shown  by  the  arrow  s,  from  the  direction  of 
the  current  to  the  direction  in  which  the  north  end  of  the 
compass  needle  would  point,1  the  screw  will  then  move  in 
the  direction  of  the  force. 

§  2.  Electromotive  force. — If  the  conductor  A  B  is  moved 
along  the  plane  in  which  o  F  E  D  lies,  its  motion  is  perpen- 
dicular to  the  forces  acting  upon  it,  and  no  work  is  done 
either  by  or  upon  A  B.  When  this  is  the  case  no  induced 
current  can  be  produced  in  A  B,  either  in  augmentation  or 
diminution  of  the  original  currents,  for  no  work  is  done  by 
the  motion  or  required  to  produce  the  motion  ;  a  current 
can  only  be  increased  by  the  exertion  of  energy  upon  it,  and 
diminished  by  expending  its  energy. 

If,  however,  the  conductor  moves  in  the  direction  o  H 
(Fig.  80),  or  across  the  dotted  lines  in  a  direction  perpen- 

1  I.e.  considering  o  as  the  centre  the  handle  would  turn  from  the  line 
O  B  to  the  line  o  NJ. 


CHAP.  IX.]        Electro-magnetic  Induction.  149 

dicular  to  the  paper  (Fig.  79),  the  motion  is  either  helped 
by  the  force  or  opposed  by  it.  To  move  the  conductor 
against  the  force,  we  must  do  work.  The  measure  of  this 
work  is  the  product  of  the  force  into  the  distance  moved 
against  it.  If  the  conductor  moves  obliquely  across  the 
lines  of  force  it  is  resisted  with  a  force  proportional  to  that 
component  of  the  motion  which  is  perpendicular  to  the  lines 
offeree,  and  the  work  done  is  equal  to  the  force  multiplied 
into  this  perpendicular  distance. 

The  work  done  on  the  conductor  is  found  by  observation 
to  be  represented  by  an  increment  or  diminution  in  the  cur- 
rent flowing  through  that  conductor  ;  now  the  work  done 
by  a  current  is  by  definition  equal  to  E  Q  =  E  c  /,  where 
E  =  the  electromotive  force  acting  between  the  ends  of  the 
conductor. 

If  a  unit  length  of  the  conductor  be  moved  a  distance  L 
across  the  lines  of  magnetic  force  in  a  field  of  intensity  H, 
the  work  done  will  be/L  =  c  H  L  :  hence,  as  the  work  done 
by  the  current  must  be  equal  to  the  work  expended  in 
moving  the  conductor,  we  have  E  c  t  —  c  H  L 


Now  j  is  the  velocity  with  which  the  conductor  is  moving, 

so  that  the  electromotive  force  per  unit  of  length  is  equal  to 
the  intensity  of  the  magnetic  field  multiplied  into  the  velo- 
city of  the  motion. 

This  law  still  holds  good  if  the  motion  be  oblique  to  the 
lines  of  force,  provided  L  be  the  component  of  the  motion 
perpendicular  to  those  lines  ;  and  if  the  conductor  A  B  was 
also  oblique  to  the  lines  of  force,  the  unit  length  must  be 
measured  perpendicular  to  those  lines  of  force.  Thus,  let 
the  direction  of  the  lines  of  force  in  a  magnetic  field  be 
represented  by  o  c^  ;  let  (Fig.  81)  a  b  be  perpendicular  to  o  o, 
in  the  plane  A  o  Oj,  let  A  a  and  B  b  be  perpendiculars  let  fall 
from  A  and  B  on  the  line  a  b,  and  let  A  B  be  moved  to 
the  position  AJ  B,,  so  that  POI;  perpendicular  to  the  plane 


Electricity  and  Magnetism.        [CHAP.  IX. 


represents  the  distance  A  B  has  moved  across  the 
lines  of  force  ;  then  the  E.  M.  F.  due  to  the  motion  will  be 
H  x  ab  x  PC* 


FIG.  8a. 


FIG.  8 1. 


C                        K 
*      fl                       fl    » 

^ 

J 

\ 

^ 

K, 

\ 

I 

K 

rt 

u      u 

1)                       F 

Observe  that  the  unit  electromotive  force  will  be  produced  by 
a  rod  of  unit  length  moving  with  unit  velocity  across  afield  of 
unit  intensity. 

§  3.  Let  there  be  two  fixed  rails  c  D  and  E  F  (Fig.  82)  in 
a  plane  perpendicular  to  the  lines  of  magnetic  force  o  QV  Let 
the  bars  A  B  and  I  K,  perpendicular  to  the  lines  of  magnetic 
force,  complete  a  closed  circuit  A  B  I  K,  round  which  a  current 
might  circulate.  Then  if  A  B  be  moved  downwards  with 
the  velocity  v,  the  electromotive  force  due  to  induction  will 
be  H  x  AB  x  v;  but  this  product  is  equal  to  the  number 
of  lines  of  magnetic  force  subtracted  from  the  area  of  the 
closed  circuit  per  unit  of  time  ;  hence,  calling  this  number  N, 

we  find  that  the  E.  M.  F.  =  — .    The  direction  of  the  current 

produced  by  this  E.  M.  F.  would  be  such  as  to  oppose  the 
motion,  i.e.  from  B  to  A.  If  i  K  were  moved  at  the  same 
rate  in  the  same  direction  there  would  be  an  equal  E.  M.  F.  in 
it,  tending  equally  to  produce  a  current  from  I  to  K,  and  this 


CHAP.  IX.]        Electro-magnetic  Induction.  151 

would  balance  the  E.  M.  F.  in  A  B,  so  that  no  current  would 
flow.  In  this  case  the  motion  of  i  K  would  add  just  as  many 
lines  of  force  to  those  crossing  the  area  A  B  c  D  as  the  motion 
of  A  B  would  subtract,  so  that  the  total  number  N  added  or 
subtracted  would  be  nil,  and  the  electromotive  force  on  the 
whole  would  also  be  nil. 

If  i  K  moves  fastest,  its  electromotive  force  would  be 
greatest,  and  the  difference  between  the  E.  M.  F.  in  i  K  and  in 

A  B  would  be  equal  to  NI  ~  N,  calling  N!  the  number  of  lines 

cut  by  i  K  during  its  motion ;  the  current  would  then  run 
round  the  parallelogram  from  i  to  K  B  A.  Similarly,  if  A  B 

moved  fastest  there  would  be  a  resultant  E.  M.  F.  =  -  ""  * 

sending  a  current  from  A  to  B  K  i.  Hence  in  both  cases  the 
E.  M.  F.  in  the  current  would  be  equal  to  the  number  of  lines 
of  magnetic  force  added  to  or  subtracted  from  the  area  per 
second,  Now  it  follows  from  the  principles  developed  in  the 
previous  paragraph  that  this  is  true  not  only  of  this  simple 
case  but  of  all  cases  whatever.  Let  the  circuit  be  of  any 
shape  whatsoever  and  moved  in  any  direction,  the  E.  M.  F. 
tending  to  send  a  current  round  the  circuit  due  to  motion 

in  a  magnetic  field  will  be  -. 

§  4.  Aii  apparatus  for  showing  the  phenomena  or  in- 
duction with  a  fixed  pair  of  rails  would  be  extremely  difficult 
to  construct ;  the  motion  could  not  be  continued  for  any 
length  of  time,  and  the  resistance  in  the  FJG 

circuit  would  vary  at  each  moment,  as 
the  stationary  portion  was  shortened 
or  lengthened  during  the  motion  of  the 
bar.  Let  a  closed  circuit  (Fig.  83)  rotate 
in  a  uniform  magnetic  field,  and  for  sim- 
plicity sake  let  us  suppose  the  field  uni- 
form, the  circuit  circular,  and  the  axis 
perpendicular  to  the  direction  of  the  lines  of  magnetic 


152  Electricity  and  Magnetism.         [CHAP.  IX. 

force.  Let  the  rotation  be  in  the  direction  of  the  hands 
of  a  watch  held  with  its  face  upwards  ;  let  the  direction 
of  the  lines  of  magnetic  force  be  perpendicular  to  the 
plane  of  the  paper,  and  such  that  a  north  pole  would 
be  impelled  from  the  spectator  down  through  the  paper. 
Consider  the  short  elements  A  B  and  c  D,  which  are  sen 
sibly  parallel  to  the  axis  and  perpendicular  to  the  lines 
of  magnetic  force.  When  these  are  just  crossing  the 
plane  of  the  paper  they  are  moving  in  the  direction  of 
the 'lines  of  magnetic  force,  and  a  current  in  them  would 
neither  be  assisted  nor  resisted  ;  but  when  the  circle  has 
made  a  quarter  of  a  turn  they  are  crossing  the  lines  of 
force  at  right  angles.  If  the  current  in  A  B  is  descending, 
the  motion  of  AB  will  be  resisted  by  the  lines  of  force,  for 
a  descending  current  in  AB  would  impel  a  north  pole  in 
front  of  the  paper  from  right  to  left,  and  would  therefore 
itself  be  repelled  from  left  to  right.  (The  north  pole  must 
be  in  front  of  the  paper  to  give  lines  of  force  which  would 
repel  a  free  north  pole  from  the  spectator  to  the  paper.) 
Hence  while  A  B  crosses  the  lines  of  force  an  E.  M.  F.  is 
produced  in  it,  tending  to  send  a  current  downwards.  The 
same  is  true  of  each  element  in  all  the  semicircle  M  A  B  N,  the 
E.  M.  F.  diminishing  in  each  element  proportionately  to  the 
sine  of  the  angle  between  the  element  and  the  lines  of 
force.  Next,  consider  the  element  CD.  This  is  simul- 
taneously crossing  the  same  lines  of  force  in  the  opposite 
direction.  This  motion  would  be  resisted  by  an  upward 
current ;  hence  the  electromotive  force  in  the  semicircle 
N  D  c  M  will  be  from  N  towards  M  or  upwards  through  this 
half  of  the  circle. 

Thus  in  both  halves  of  the  circle  the  E.  M.  F.  tends  to 
produce  a  current  moving  from  M  to  A  B,  N,  D  c,  and  back 
to  M. 

This  electromotive  force  will  evidently  be  strongest  at 
all  points  of  the  circle  when  this  is  crossing  the  lines  of 
force  at  right  angles,  i.e.  when  the  plane  of  the  circle  is  in 


CHAP.  IX.]          Electro-magnetic  Induction.  153 

the  direction  of  the  lines  of  force.  It  will  begin  feebly  as 
the  circle  in  its  rotation  leaves  the  position  sketched  and 
advances  as  shown  by  the  arrow,  for  at  first  the  inclination 
of  the  direction  of  each  element  to  the  lines  of  force  will  be 
small ;  and  again,  after  reaching  its  maximum,  this  inclination 
diminishes  until  it  becomes  nil  after  half  a  turn  has  been 
made.  During  the  next  half-turn,  while  M  A  B  N  is  behind 
the  paper,  the  E.  M.  F.  will  tend  to  send  current  up  from  A  to 
M  through  B  A;  the  direction  of  the  current  will  therefore, 
during  this  half-turn,  be  reversed  in  the  material  circuit. 
Relating  to  a  fixed  exterior  point,  the  current  is,  however, 
always  in  one  direction,  though  varying  from  zero  to  a 
maximum  at  every  half-revolution.  The  circuit  might  evi- 
dently be  not  a  single  circle  but  a  coil  of  wire.  The  E.  M.  F. 
would  increase  with  the  length  of  the  coil.  If,  however,  the 
only  resistance  be  that  of  the  coil,  the  current  will  be 
constant  whatever  number  of  turns  were  taken,  for  the 
resistance  will  increase  in  the  same  proportion  as  the  elec- 
tromotive force.  If  some  exterior  constant  resistance  be 
connected  with  the  coil,  by  sliding  contacts  near  the 
axis,  the  current  will  be  larger  with  many  than  with 
few  turns. 

There  is  no  difficulty  in  calculating  the  exact  electromotive 
force  due  to  a  coil  of  any  given  shape  rotating  in  any  mag- 
netic field,  except  the  mathematical  difficulty  of  summing 
up  the  different  E.  M.  F.  in  all  the  different  elements  of  the 
coil  at  each  moment,  or,  what  comes  to  the  same  thing, 
determining  the  value  of  N  during  the  motion. 

It  is  now  clear  that  the  electromotive  force  produced  by 
the  motion  of  a  closed  circuit  in  a  magnetic  field  of  known 
intensity  can  be  expressed  in  terms  of  that  intensity  and  of 
velocity  only ;  this  measurement  gives  the  value  of  the  E.  M.  F. 
in  absolute  electromagnetic  measure.  We  have  also  seen 
bow  to  measure  the  value  of  any  current  c  in  the  same 

measure,  and  since    R  =   5  in  any  circuit,  the  resistance  R 


1  54  Electricity  and  Magnetism.         [CHAP.  IX. 

of  that  circuit  can  be  experimentally  determined  by  measur- 
ing the  values  of  E  and  c.  When  the  resistance  of  a  single 
circuit  has  been  thus  ascertained,  a  material  standard  coil 
equal  to  some  multiple  of  the  absolute  unit  can  be  prepared 
by  comparison  with  this  experimental  circuit.  When  this 
has  been  done  once  for  all,  the  resistance  of  other  conductors 
can  be  easily  determined  by  comparison  with  this  standard. 
The  following  statements  describe  the  experiments  by  which 
such  a  standard  has  been  prepared. 

§  5.  Let  us  consider  a  circular  coil  of  radius  K  rotating  with  an 
angular  velocity  A  in  a  field  of  the  intensity  H.  Then  during  each  half- 
revolution  the  number  N,  equal  to  it  K2  H,  will  be  alternately  added  and 
subtracted.  Every  addition  and  subtraction  tends  to  send  a  current  in 
the  same  direction  relatively  to  an  external  point.  Let  n  be  the  number 

of  turns  per  second,  then  n  =  —  ,  and  the  total  number  of  lines  of  force 
added  and  subtracted  per  second  will  be  4  v  K2H 

2T 

The  E.  M.  F.  due  to  this  will  be  2  A  K2H,  and  the  equivalent  current 
produced  -  ,  where  R  is  the  resistance  of  the  circuit.  If  there  be 

R 

m  turns  the  length  of  the  wire  in  the  coil  L  =  2*  Km,  and  the  area 
enclosed  =  IT  K*m  =  —  .  The  number  of  lines  added  per  second  ex- 


pressed in  this  manner  will  be  —        and  the  current 

7T  7T  R 

current  may  be  measured  on  a  stationary  electrodynamometer  or  gal- 
vanometer, and  when  it  has  been  thus  measured  in  absolute  measure 
the  only  remaining  unknown  quantity  is  R. 

§  6.  The  determination  of  R  by  this  method  requires  a  knowledge 
of  the  intensity  of  the  magnetic  field  H,  and  a  contemporaneous  measure- 
ment of  the  absolute  value  of  a  current. 

These  two  observations  can  be  dispensed  with  by  hanging,  accord- 
ing to  Sir  William  Thomson's  method,  a  small  magnet  in  the  centre  of 
the  rotating  coil  and  observing  its  deflection.  The  induced  currents 
will  all  deflect  this  magnet  in  the  direction  of  the  rotation  of  the  coil  ; 
the  couple  exerted  on  a  magnetic  needle  of  the  moment  m  /,  when 

deflected  to  ihe    angle  d,  will  be  L'AH  m  I  cos  d.     The  equal  and 

4  K2R 


CHAP.  IX.]          Electro-magnetic  Induction.  155 

opposite  couple  exerted  by  the  earth's  magnetism  will  be  H  m  I  sin  d  ; 
hence 


This  gives  a  simple  expression  for  the  resistance  of  the  circuit  in 
absolute  measure  in  terms  of  known  and  simple  magnitudes.  In  prac- 
tically making  the  experiment  several  corrections  have  to  be  introduced, 
as  for  the  inductive  effects  of  the  magnet  on  the  coil.  The  experiment 
was  carefully  carried  out  by  a  committee  of  the  British  Association,  and 
the  absolute  resistance  of  a  certain  standard  determined  in  this  way  serves 
to  determine  the  absolute  resistance  of  any  other  circuit. 

§  7.  When  the  induction  takes  place,  not  in  consequence 
of  the  motion  of  a  wire  in  a  magnetic  field,  but  in  con- 
sequence of  the  sudden  creation  of  a  magnetic  field,  as 
when  a  neighbouring  current  is  suddenly  commenced,  the 
effect  is  exactly  as  if  the  wire  had  been  suddenly  moved 
from  an  infinite  distance  to  its  actual  position  on  the  new 
magnetic  field.  The  electromotive  force  is  in  this  case  also 

equal  to  ~,  where  N  is  the  additional  number  of  lines  of 

magnetic  force  introduced  into  the  circuit  in  the  time  t  ; 
when  the  induction  takes  place  in  consequence  of  the  cessa- 
tion of  a  current,  the  electromotive  force  is  in  the  opposite 

direction,  and  is  equal  to  -  ;  where  N  is  the  number  of  lines 

withdrawn.  If  t  be  made  very  small,  the  E.  M.  F.  tending  to 
produce  an  induced  current  may  be  indefinitely  increased  ; 
and  similarly  if  a  current  can  be  made  to  reach  its  full  strength 
in  a  very  short  time,  it  will  produce  an  E.  M.  F.  in  a  wire  close 
beside  it  much  greater  than  that  required  to  produce  the 
original  current.  The  wire  in  which  the  inducing  current 
circulates,  is  often  called  the  primary  wire;  the  one  in 
which  the  current  is  induced  is  called  the  secondary  wire. 
§  8.  In  order  to  determine  the  electromotive  force 


156  Electricity  and  Magnetism.         [CHAP.  IX 

produced  in  a  secondary  circuit  by  the  commencement  or 
cessation  of  a  current  c  in  a  primary  circuit,  we  require  to 
calculate  the  number  N  of  lines  of  force  produced,  cutting 
the  surface  inclosed  by  the  secondary  circuit.  (Of  course 
lines  of  force  going  in  opposite  directions  through  the 
surface  must  be  reckoned  positive  and  negative,  and  their 
addition  made  accordingly.)  This  number  N  divided  by  t 
gives  the  electromotive  force.  It  is  extremely  difficult  to 
determine  /,  for  no  current  begins  instantaneously,  and  the 
laws  of  its  increase  are  extremely  complex.  The  fact  that 
the  current  is  employed  to  induce  a  current  or  currents  in 
secondary  conductors,  increases  /.  The  statical  induction, 
.when  sensible,  increases  /,  and  magnetisation  due  to 
currents  increases  t.  The  actual  determination  of  the 
E.  M.  F.  in  any  secondary  circuit  will  not  be  here  attempted, 
but  the  notions  given  serve  to  show  how  we  may  increase 
or  diminish  this  E.  M.  F.  in  designing  inductive  apparatus. 

§  9.  I  have  now  shown  how,  theoretically,  resistance,  elec- 
tromotive force,  and  currents  can  all  be  measured  in  abso- 
lute electro-magnetic  measure.  Quantity  can  be  measured 
either  by  observing  the  total  current  which  it  produces 
when  flowing  away,  for  which  purpose  a  simple  method 
will  hereafter  be  given,  depending  on  the  use  of  galvano- 
meters, or  it  may  be  measured  by  observing  its  electro- 
static effects,  and  being  then  known  in  electrostatic  measure, 
it  may  be  converted  into  electro-magnetic  measure  by  mul- 
tiplication into  the  constant  28,225.000,000.  Capacity  is 
obtained  by  observing  the  quantity  which  the  given  con- 
ductor contains  when  electrified  to  a  potential  E.  Theo- 
retically, therefore,  we  may  be  said,  while  studying  the  laws  of 
electro-magnetic  induction,  to  have  discovered  how  it  is  pos- 
sible to  measure  all  electrical  magnitudes  in  this  series  of 
units.  The  practical  methods  adopted  will  be  described 
hereafter. 

§  10.  The  examples  given  of  the  modes  of  calculating 
induced  currents  in  the  two  simple  cases  of  a  straight  bar 


CHAP.  IX.]         Electro-magnetic  Induction.  157 

moving  across  a  uniform  field,  and  a  circular  coil  rotating 
in  such  a  field,  serve  to  show  how  all  similar  problems  must 
be  attacked.  The  exact  solution  of  them  requires  mathe- 
matical analysis  of  the  highest  kind ;  but  correct  views  of 
the  general  nature  of  the  effects  to  be  expected  are  very 
readily  obtained  from  the  general  elementary  propositions 
now  laid  down.  Thus  it  is  easy  to  examine  whether  the 
electromotive  force  in  some  parts  of  the  circuit  is  acting  in 
a  direction  opposed  to  that  in  others ;  if  so,  it  is  easy  to  see 
that  to  reduce  the  opposing  action  we  must  reduce  the 
velocity  of  those  parts,  and  place  them  in  the  weakest  por- 
tion of  the  magnetic  field,  while  the  efficient  portions  of  the 
circuit  must  be  placed  in  the  strongest  portions  of  the  field, 
and  made  to  move  with  the  greatest  velocity.  The  best 
direction  of  motion  is  also  easily  ascertained.  The  general 
effect  of  adding  to  the  length  of  the  wire  or  coil  in  which 
induction  is  taking  place  is  also  easily  perceived,  and  the 
object  of  making  the  coil  of  materials  which  have  but  little 
electrical  resistance.  Increasing  the  thickness  of  the  wire 
does  not  at  all  increase  the  electromotive  force,  but  inas- 
much as  it  diminishes  the  resistance,  a  thick  and  short  wire 
may  give  a  very  considerable  current,  if  outside  the  moving 
coil  there  be  no  considerable  additional  resistance  to  over- 
come. But  if  we  desire  a  considerable  or  even  sensible 
current  through  an  external  wire  of  great  length,  or  of  great 
resistance,  then  our  inducing  coil  must  be  long  in  order  to 
give  great  E.  M.  F.,  and  in  such  a  case  its  internal  resistance 
will  not  greatly  diminish  the  current,  because  it  will  not 
greatly  increase  the  resistance  of  the  whole  circuit.  If  cur- 
rents of  very  short  duration  are  required,  we  may  move  our 
coil  or  wire  rapidly  across  a  magnetic  field  of  small  size  but 
great  intensity,  whereas  if  a  current  of  longer  duration  is 
required,  the  motion  must  be  prolonged,  and  it  will  be  neces- 
sary to  have  a  large  magnetic  field. 


158  Electricity  and  Magnetism.          [CHAP.  X. 


CHAPTER  X. 

UNITS    ADOPTED    IN   PRACTICE. 

§  1.  IN  the  last  chapter  I  have  described  the  manner  in 
which  the  strength  of  a  current  may  be  measured  in  electro- 
magnetic measure.  The  method,  although  not  offering  any 
extreme  difficulty,  is  yet  too  complex  for  continual  use, 
and  currents  will  certainly  not  be  commonly  expressed  in 
this  manner,  until  electrodynamometers  are  habitually  sold 
of  such  construction  that  by  simply  multiplying  the  observed 
deflection  into  a  constant  number,  the  strength  of  the 
current  is  obtained. 

The  direct  measurements  of  electromotive  force  and  of 
resistance  in  the  same  series  of  units  are  still  more  com- 
plex. It  is  unnecessary  that  each  electromotive  force  or 
resistance  should  be  directly  measured  in  absolute  measure 
by  these  complicated  methods.  A  standard  of  electrical 
resistance  approximately  equal  to  one  thousand  millions 
of  absolute  units  of  resistance  (centimetre,  gramme,  second) 
has  been  prepared  by  a  committee  of  the  British  Associa- 
tion. This  standard  is  an  actual  wire  of  the  required  re- 
sistance. The  measurement  of  any  other  resistance  x 
in  absolute  measure  consists,  therefore,  in  a  comparison 
of  x  with  this  standard  or  a  copy.  The  process  in  this 
case  is  the  same  as  that  of  measuring  length  in  metres. 
Theoretically  the  measurement  of  a  length  x  in  metres 
means  the  comparison  of  x  with  a  certain  diameter  of  the 
earth ;  practically  it  means  the  comparison  of  x  with  a 
measure  authorized  by  Government  to  be  called  a  metre. 

§  2.  The  standard  of  resistance  has  been  called  an  ohm, 
and  is  now  in  common  use. 

Gauges  of  electromotive  force  ought  for  similar  reasons  to 
be  issued,  and  might  be  of  various  forms.  Thus  the  gauge 
might  indicate  a  given  difference  of  potential  in  virtue  of  the 


CHAP.  X.]  Units  adopted  in  Practice.  159 

attraction  which  two  opposed  plates  exert  on  one  another, 
or,  even  more  roughly,  in  terms  of  the  distance  at  which 
sparks  pass  across  air  between  two  given  balls.  There  can 
be  no  doubt  that  within  a  few  years  gauges  of  this  kind 
will  be  issued  with  the  same  authoritative  stamp  as  attaches 
to  the  ohm.  Meanwhile  electromotive  force  or  difference 
of  potential  is  often  expressed  in  terms  of  the  electro- 
motive force  produced  by  the  special  form  of  voltaic 
battery  known  as  the  Daniell's  cell.  The  E.  M.  F.  of  this 
cell  is  about  100,000,000  absolute  units,  centimetre,  gramme, 
second,  and  is  fairly  uniform.  A  much  better  standard  of 
electromotive  force  is  the  cell  introduced  by  Mr  Latimer 
Clark,  and  described  by  him  as  follows,  (Proceedings  R.  S. 
No.  136,  1872)  :  'The  battery  is  composed  of  pure  mercury 
as  the  negative  element,  the  mercury  being  covered  by  a 
paste  made  by  boiling  mercurous  sulphate  in  a  thoroughly 
saturated  solution  of  zinc  sulphate,  the  positive  element 
consisting  of  pure  zinc  resting  on  the  paste.'  '  Contact  with 
the  mercury  may  be  made  by  means  of  a  platinum  wire.' 
'The  element  is  not  intended  for  the  production  of  currents, 
for  it  falls  immediately  in  force  if  allowed  to  work  on  short 
circuit.  It  is  intended  to  be  used  only  as  a  standard  of 
electromotive  force  with  which  other  elements  can  be  com- 
pared by  the  use  of  the  electrometer,  or  condenser,  or  other 
means  not  requiring  the  use  of  a  prolonged  current.'  The 
electromotive  force  of  this  cell  is,  in  electro-magnetic  units, 
i'457xio8  (centimetre,  gramme,  second),  or  i^yxio5 
(metre,  gramme,  second).  There  is  already  a  unit  of 
electromotive  force  in  practical  use  called  a  volt.  The  volt  is 
intended  to  represent  io8  absolute  units,  centimetre,  gramme, 
second  ;  the  E.  M.  F.  of  Latimer  Clark's  cell  is  1*457  volt. 

The  capacity  of  a  given  conductor  can  be  determined  in 
absolute  measure  with  less  trouble  than  either  the  electro- 
motive force  or  the  resistance,  and  condensers  of  the 

approximate  capacity  of  10,000,000.000,000  or  I0~13  absolute  units, 
and  called  microfarads,  are  in  common  use. 


160  Electricity  and  Magnetism,          [CHAP.  x. 

§  3.  We  thus  find  that  in  ordinary  electrical  measure- 
ments, even  when  we  require  to  calculate  the  relations 
between  forces,  work,  or  heat  and  electrical  magnitudes,  we 
need  only  compare  these  electrical  magnitudes  with  known 
standards,  these  standards  having  been  chosen  with 
distinct  reference  to  the  units  of  force  and  work.  To  the 
ordinary  electrician  it  is  therefore  much  more  important  to 
know  how  to  compare  accurately  one  resistance  with  an- 
other, one  current  with  another,  and  so  forth,  than  to  be 
able  to  determine  resistances  or  currents  in  absolute  mea- 
sure. Indeed,  when  an  electrician  is  said  to  measure  a 
current  or  a  resistance,  it  is  this  comparison  with  a  re- 
cognised unit,  which  is  in  all  cases  understood.  The 
unit  employed  is  important  only  so  far  as  it  is  widely 
adopted  and  allows  a  more  or  less  ready  application  of 
the  measurement  in  formulae,  involving  other  electrical 
magnitudes.  The  series  of  units  most  generally  adopted  in 
Great  Britain  have  received  distinctive  names,  and  are  all 
based  on  the  absolute  system.  They  are,  however,  all 
multiples  or  submultiples  of  the  absolute  units,  which  are 
themselves  of  inconvenient  magnitudes. 

§  4.  The  unit  of  resistance  is  termed  an  ohm  and  =  io9 
absolute  units  (centimetre,  gramme,  second). 

The  unit  of  electromotive  force  is  termed  a  volt  =  io8 
absolute  units. 

The  unit  of  capacity  is  termed  a  farad  =  - — .absolute  unit. 

io9 

The,  unit  of  quantity  is  that  which  will  be  contained  in 
one  farad  when  electrified  to  the  potential  of  one  volt: 
it  has  no  distinctive  name,  and  may  be  called  a  farad 
also.1  This  unit  of  quantity  =  yV  absolute  unit.  The 
absolute  units  referred  to  throughout  are  those  based  on  the 
centimetre,  gramme,  and  second.  There  is  a  strong  objec- 
tion to  the  use  of  the  words  absolute  unit,  inasmuch  as  they 
do  not  indicate  the  series  of  fundamental  units  on  which 

1  Mr.  Latimer  Clark  calls  it  a  Weber. 


CHAP  X.]  Units  adopted  in  Practice.  161 

the  derived  unit  is  based.  The  volt,  farad,  and  ohm  are 
free  from  this  ambiguity. 

The  unit  of  current  is  one  farad  per  second ;  it  is  one- 
tenth  of  the  absolute  unit  of  current,  and  is  frequently 
termed  for  brevity  a  farad,  just  as  in  speaking  of  velocity 
we  often  speak  of  a  velocity  of  100  feet,  the  words  per 
second  being  understood. 

§  5.  Inasmuch  as  the  electrician  deals  with  magnitudes 
differing  in  greatness  very  widely  from  one  another,  it  is 
convenient  to  use  multiples  and  submultiples  of  the  above 
units,  each  having  its  appropriate  name. 

The  megavolt    =  one  million  volts. 

„    megafarad  =  „  farads. 

„    megohm     =  '  „  ohms. 

Similarly, 

The  microvolt   =  one  millionth  of  a  volt. 
„   microfarad  =  „          ,,     farad. 

„   microhm     =  „         of  an  ohm. 

The  following  table  (p.  162)  gives  the  value  of  each  unit 
in  three  systems  of  absolute  units,  in  which  the  metre, 
centimetre,  and  millimetre,  and  in  a  fourth  in  which  the  milli- 
gramme is  substituted  for  the  gramme,  are  respectively  made 
the  basis  or  starting-point. 

When  we  require  to  convert  measurements  expressed  to 
absolute  units  based  on  any  given  system  of  fundamental 
units  into  absolute  measurements  based  on  some  other 
system,  it  is  necessary,  in  order  to  calculate  the  multiplier  or 
divisor  to  be  used  for  the  conversion,  that  we  should  know 
what  are  called  the  dimensions  of  the  units.  In  other  words, 
we  must  know  at  what  power  each  fundamental  unit  enters 
into  the  particular  derived  unit ;  thus,  in  the  case  of  velo- 
city, which  is  perhaps  the  simplest  derived  unit,  the  dimen- 
sions are  said  to  be  - ,  or  a  length  divided  by  an  interval 

of  time,  because  the  magnitude  of  the  unit  is  directly  pro- 

M 


162 


Electrtcuy  and  Magnetism.  [CHAP.  X. 


281! 


J3  i"  C  g. 

H*«|H 


CHAP.  X.]  Units  adopted  in  Practice.  163 

portional  to  the  magnitude  of  the  unit  used  to  measure 
length,  and  inversely  proportional  to  that  of  the  unit  used 
to  measure  time.  Similarly  the  absolute  unit  of  force  is 
directly  proportional  to  the  unit  of  length  and  the  unit  of 
mass  employed  ;  it  is  inversely  proportional  to-  the  square 
of  the  unit  of  time  used  ;  hence  the  dimensions  of  the  unit 

T  AT 

of  force  are  —  . 

T2 

When  we  wish  to  convert  a  measurement  expressed  in 
absolute  units  based  on  the  units  L,  M,  T,  (say  foot,  grain, 
second)  into  an  absolute  measurement  based  on  some  other 
system  of  units  /,  m,  /,  (say  metre,  gramme,  second),  we 

require   to  know  the  ratios  -,     -,     -,   of  the  actual  mag- 

/     m     t 

nitudes  of  each  pair  of  units.     Thus  in  the  example  chosen 

-  =  0*3048,  —  =  '0648,  -  =  1  ;  then  to  effect  the  conver- 
/  m  t 

sion  from  English  to  French  measure  we  must  multiply  the 
number  expressing  the  measurement  in  English  measure  by 
each  ratio  raised  to  the  power  at  which  the  corresponding 
letter  appears  in  the  expression  for  the  dimensions  of  the 
unit.  If  the  power  is  negative,  we  divide  by  the  ratio 
instead  of  multiplying  ;  thus  to  convert  a  velocity  expressed 
in  English  measure  into  a  velocity  in  French  measure,  we 
multiply  by  0-3048,  and  divide  by  1  :  to  convert  a  measure 
of  force  (foot,  grain,  second)  into  French  measure  we  multi- 

,    -,     "3048  x  '0648 
ply  by  -^  --  ^p—        =  -01975. 

The  following  table  of  dimensions  and  constants  is  taken 
from  the  British  Association  Report  on  Electrical  Standards^, 
1863. 

Fundamental  Units. 

Length  =  L.     Time  =  T.     Mass  =  M. 

Derived  Mechanical  Units. 


=  eocy  =  V  - 

T* 

M  2 


Work   =  w   =  i^1.  Force   =  F  =  ^     Velocity  =  V  -   ~. 
T2  T*  T 


164 


Electricity  and  Magnetism.  [CHAP.  X. 


Derived  Magnetic  Units. 

Strength  of  the  pole  of  a  magnet  .  .  .  »/ 
Moment  of  a  magnet  .....  ml 
Intensity  of  magnetic  field  .  .  .  .  H  = 

Electro-magnetic  System  of  Units. 
Quantity  of  electricity  .         .....  Q 

Strength  of  electric  current    .....  c 


L*  T-I 
L?  T~l 
~i  T"1 


Electromotive  force       . 
'Resistance  of  conductor 


E  = 
R  = 


T"1 


L  T-1 


Electrostatic  System  of  Units. 
Quantity  of  electricity   ...... 

Strength  of  electric  currents  .... 

Electromotive  force 

Resistance  of  conductor         .... 


.  q  =  L?  T-1  M* 
.  C  =  L*  T"2  M^ 
.  e  =  L*  T-1  M^ 

.    r  ---  L~i  T 

Table  for  the  conversion  of  British  (foot  grain  second]   system   to 
centimetrical  (centimetre  gramme  second]  system. 


Number  of 
centimetrical 
units 
contained  in  a 
British  unit. 

Log. 

Log. 

Number  of 
British  units 
contained  in  a 
centimetrical 
unit. 

\.   For  M 

0-0647989 

2~-8i  15678 

1-1884321 

I5-43235 

2.  For  L,  v,  R,  i&  v 

30-47945 

1-4840071 

2~-5i59929 

•03280899 

3.  For  F    (also   for  1 
foot  grains  and  > 
metregrammes  J 

I  -97504 

0-2955749 

i  7044250 

•506320 

4.   For  w 

60-198 

I-7795820 

2-2204179 

•Ol66ll85 

5.  For  H  and  elec  1 
tro  -  chemical  > 
equivalents        J 

•0461085 

2-6637804 

1-3362196 

21-6880 

6.   For  Q,  C  and  e  . 

I  -40536 

0-1477874 

7-8522125 

•7II56I 

7.  For  E  m  q  and  e 

42*8346 

1-6317949 

2-3682051 

•0233456 

8.  For  heat    - 

0-0359994 

2-5562953 

i  -4437046 

27-7782 

British  system. — Relation  between  absolute  and  other  ttnits. 


C 


^aa 

>/  ,/ 

,j^d.  *_±±_      ,  z 

2.^^     ^" 


-  Z 


</_^<^s. 


CHAP.  X.]  Units  adopted  in  Practice.  165 

Let  v  be  the  ratio  of  the  electro-magnetic  to  the  electrostatic  unit  of 
quantity  =  28-8  x  io9  centimetres  per  second  approximately,  and  we 
have 


a  =  vQ\<:--=vc\e=--E\      r  =- 
I  I  v      \  v 


London. 


!n  London  ,  3*  '.889  abso.u.e  units  of 

One  absolute  /  force  \  _  1  /unit  weight  1  evervwhere- 

unit  of         \  work  J      g  I  unit  weight  and  unit  length  /  evevw 

£•  in  British  system  =  32*088  (1  +  0-005133  sin2  \  ),  where  A  =  the 
latitude  of  the  place  at  which  the  observation  is  made. 

Heat.  The  unit  of  heat  is  the  quantity  required  to  raise  the  temper- 
ature of  one  grain  of  water  at  its  maximum  density  i°  Fahrenheit. 

Absolute  mechanical  equivalent  of  unit  of  heat  =  24861  =  772  foot 
grains  at  Manchester. 

Thermal  equivalent  of  an  absolute  unit  of  work  ==  '000040224. 

Thermal  equivalent  of  afoot  grain  at  Manchester  =   -0012953. 

Electro-chemical  equivalent  of  water  =  -02  nearly. 

Metrical  system.  Relation  between  absolute  and  other  units.  (Centi- 
metre gramme  second.  ) 

One  absolute  /force  1  /weight  of  a  gramme! 

unit  of         ^workj  yD     ^  centimetre  gramme   / 

\4.-n    •     /the  weight  of  a  gramme"!        ^Q^.Q^Q  /absolute  "1  force. 
At  Parls  (or  centimetre  gramme    /  =  98o'8(8  {.^  of  j>  wQrk 

One  absolute  /force  "I  _  I   /unit  weight  >  , 

unit  of        \workj  ~  ^  \unit  weight  x  unit  length  $  e 

^•in  metrical  system  —  978-024  (i  +  0-005133  sin2  A),  where  A  =  the 
latitude  of  the  place  where  the  experiment  is  made. 

Heat.  The  unit  of  heat  is  the  quantity  required  to  raise  one  gramme 
of  water  at  its  maximum  density  i°  centigrade. 

Absolute  mechanical  equivalent  of  the  unit  of  heat  =  41572500  = 
42354-2  centimetre  grammes  at  Manchester. 

Thermal  equivalent  of  an  absolute  unit  of  work  =  -000000024054. 

Thermal  equivalent  of  a  centimetre  gramme  at  Manchester  = 
•0000236154. 

Electro-chemical  equivalent  of  water  =  -00092  nearly. 


1 66  Electricity  and  Magnetism.         [CHAP.  XI. 


CHAPTER   XI. 

CHEMICAL  THEORY  OF  ELECTROMOTIVE  FORCE. 

§  1  IN  Chapter  III.  §  1 5,  the  phenomenon  of  electrolysis 
was  described  and  water  was  shown  to  be  an  electrolyte ;  the 
decomposition  of  water  is  much  facilitated  by  the  addition 
of  a  little  acid,  which  has  the  effect  of  diminishing  the 
resistance  of  the  liquid  and  of  allowing  a  larger  current  to 
pass  from  a  given  battery  than  would  traverse  pure  water. 
The  acid  is  not  decomposed,  or,  if  it  is,  the  elements  re- 
combine  so  as  never  to  appear  at  the  electrodes,  as  the 
metal  terminals  plunged  in  the  liquid  are  called.  Platinum 
or  gold  electrodes  are  used  to  show  the  decomposition  of 
water  ;  otherwise  the  oxygen  carried  to  the  positive  electrode 
would  not  be  set  free,  but  would  oxidise  the  metal  instead 
of  appearing  in  the  test  tube  (Fig.  41).  Three  or  four 
galvanic  cells  are  usually  employed  to  decompose  water. 
The  electromotive  force  of  one  of  the  usual  Daniell's  cells 
is  insufficient  for  the  purpose,  and  this  we  shall  be  able  to 
prove  from  a  consideration  of  the  chemical  affinity  of  the 
materials  employed,  and  of  the  work  required  to  be  done, 
measured  in  absolute  measure.  When,  the  tubes  are  gra- 
duated so  that  the  volume  of  the  gases  can  be  measured,  the 
apparatus  shown  in  Fig.  41  is  called  a  voltameter.  Owing 
to  the  absorption  of  gas  by  the  water,  neither  the  true 
relative  nor  absolute  volumes  of  the  gases  appear  in  the 
test  tubes. 

With  very  few  exceptions,  electrolysis  occurs  only  in 
liquids.  Fused  saline  bodies  are  electrolytes,  and  probably 
many  fused  oxides  are  electrolytes,  but  the  reoxidation 
takes  place  so  readily  that  this  is  not  easily  verified. 
Conduction  through  electrolytes  is  subject  to  Ohm's  law, 


CHAP.  XL]  Chemical  Theory  of  Electromotive  Force.  167 

so  far  as  is  known.  Electrolytes  apparently  conduct  very 
small  currents  without  being  decomposed. 

§  2.  Electrolytes  are  not  necessarily  decomposed  into 
simple  or  elementary  substances.  Many  electrolytes  are 
decomposed  into  two  groups  of  components;  each  group,  or 
each  simple  element,  is  called  by  Faraday  an  ion  ;  with  any 
given  electrolyte,  the  same  group,  or  ion,  always  appears  at 
the  same  electrode,  so  that  ions  may  be  classed  as  electro- 
positive or  electronegative  ;  the  electropositive  ion  appears 
at  the  negative  electrode,  and  the  electronegative  ion  at  the 
positive  electrode. 

When  the  electrolyte  is  changed,  an  ion  may  change  its 
electrode,  and  ions  can  be  classed  in  a  list  such  that  each  is 
electropositive  to  all  which  follow ;  so  that  an  ion  such  as 
sulphur,  which  is  electronegative  towards  hydrogen,  is  electro- 
positive towards  oxygen. 

'  Hydrogen  and  metals  are  electropositive  relatively  to 
acids  and  oxygen :  oxygen  is  the  most  electronegative,  and 
potassium  the  most  electropositive  element. 

§  3,  The  bases  of  salts  may  practically  be  classed  as 
electropositive  ions.  When  we  decompose  salts  composed 
of  two  or  of  three  elements,  we  find  the  base  at  the 
negative  electrode  and  the  acid  at  the  positive  electrode ; 
but  this  classification  is  not  strictly  scientific,  for  chemists  do 
not  consider  the  decomposition  of  sulphate  of  potassium,  foi 
instance,  as  consisting  in  the  separation  of  the  base  potash 
from  the  "sulphuric  acid,  but  rather  as  the  separation  of 
potassium  from  the  other  constituents  of  sulphate  of  potash. 
When,  however,  the  potassium  appears  at  the  negative  pole, 
it  decomposes  water  and  combines  with  oxygen  to  form 
potash,  while  at  the  other  pole  sulphuric  acid  and  one 
element  of  oxygen  appear.  When  the  decomposition  goes 
on  rapidly,  oxygen  and  hydrogen  in  small  quantities  do 
appear  at  each  electrode;  otherwise  they  recombine  and 
form  water.  The  practical  result  is  that  the  base  behaves  as 
an  electropositive  and  the  acid  as  an  electronegative  ion. 


1 68  Electricity  and  Magnetism.         [CHAP.  XI. 

§  4.  The  following  table  is  an  electro-chemical  series, 
in  which  the  most  electropositive  materials  come  last : — 

Oxygen  Chromium  Silver  Manganese 

Sulphur  Boron  Copper  Aluminium 

Nitrogen  Carbon  Bismuth  Magnesium 

Fluorine  Antimony  Tin  Calcium 

Chlorine  Silicon  Lead  Barium 

Bromine  Hydrogen  Cobalt  Lithium 

Iodine  Gold  Nickel  Sodium 

Phosphorus  Platinum  Iron  Potassium 

Arsenicum  Mercury  Zinc 

§  5,  The  quantity  of  any  electrolyte  decomposed  by  a 
current  is  proportional  to  the  strength  of  the  current  and  to  its 
duration  ;  in  other  words,  to  the  whole  quantity  of  electricity 
which  during  decomposition  passes  through  the  electrolyte. 

The  weights  of  different  electrolytes  decomposed  by  a 
constant  current  are  in  direct  proportion  to  their  combining 
numbers.  Tables  of  these  numbers  are  given  in  all  works 
on  chemistry. 

It  follows  from  the  above  propositions  that  if  we  know  the 
weight  of  any  electrolyte  which  has  been  decomposed  by 
any  known  current  in  a  known  time,  we  can  calculate  the 
weight  of  any  other  electrolyte  which  in  a  given  time  will 
be  decomposed  by  any  given  current.  It  does  not  follow  that 
a  given  battery  will  decompose  two  electrolytes  at  such  rates 
that  the  quantities  decomposed  in  a  given  time  are  simply 
proportional  to  the  combining  numbers  ;  the  resistance  of 
one  electrolyte  may  be  so  different  from  that  of  the  other, 
that  in  order  to  obtain  the  same  current  very  different 
batteries  may  be  required  in  the  two  cases. 

The  quantity  of  each  electrolyte  decomposed  by  the  unit 
current  in  a  second  is  perfectly  definite  and  constant ;  we 
shall  denote  this  quantity  by  the  symbol  t,  and  call  it  the 
electro-chemical  equivalent  of  the  substance.  Since  the  weights 
of  the  electrolytes  decomposed  by  the  unit  current  are  pro- 
portional to  the  combining  numbers  of  the  compounds, 


CHAP.  XI.]  Chemical  Theory  of  Electromotive  Force.  169 


the  weights  of  the  ions  appearing  at  each  electrode  will  be 
proportional  to  these  numbers,  and  hence,  knowing  the 
weight  of  any  one  ion  produced  at  either  electrode  by  the 
unit  current  in  a  given  time  we  can  calculate  the  weights  of 
all  the  others ;  in  other  words,  we  can  calculate  the  electro- 
chemical equivalent  of  each  ion,  and  therefore  of  all  simple 
bodies.  The  following  is  a  table  of  the  electro-chemical 
equivalents  of  some  bodies  expressed  in  grammes  and 
calculated  from  that  of  water  experimentally  determined  to 
be  -00092';  that  is  -to  say,  the  table  is  calculated  on  the 
assumption  that  one  absolute  electro-magnetic  unit  of  current 
(centimetre  gramme  second)  will  in  one  second  decompose 
•00092  gramme  of  water. 


Aluminium 
Antimony  . 
Arsenicum 
Barium 
Bismuth     . 
Boron 
Bromine     . 
Calcium 
Carbon 
Chlorine    . 
Chromium . 
Cobalt 
Copper 
Fluorine     . 
Gold 

Hydrogen  . 
Iodine 


•00141 

Iron  . 

•00624 

Lead 

•00383 

Magnesium 

•00700 

Manganese 

•01073 

Mercury     . 

•00056 

Nickel 

•00409 

Nitrogen    . 

•00204 

Oxygen 

•00061 

Phosphorus 

•00181 

Platinum    . 

•00268 

Potassium  . 

•00301 

Silicon 

•00324 

Silver 

•00097 

Sodium 

•01007 

Sulphur 

•oooio 

Tin    . 

•00649 

Zinc  . 

•00186 
•01058 
•00123 
•00280 

•OIO22 
•OO3OI 
•OOO72 
•OOO82 
•00158 
•01007 
•00199 
•00143 
•00552 
•OOIlS 
•00164 
•00604 
•00342 


§  6.  When  a  current  is  passed  from  metal  electrodes 
through  an  electrolyte  and  decomposes  it,  the  current  per- 
forms an  action  equivalent  to  the  performance  of  work  or 
expenditure  of  energy — an  action  which  may  be  measured  in 
the  units  employed  to  measure  energy.  Let  i  be  the  electro- 
motive force  between  the  two  electrodes,  and  Q  the  quantity 
of  electricity  passing,  then  the  work  done  by  the  electricity 


1  70  Electricity  and  Magnetism.          [CHAP.  XI. 

is,  as  we  know,  necessarily  equal  to  I  Q  ;  and  if  this  energy  is 
wholly  spent  in  decomposing  the  electrolyte,  this  product 
measures  the  energy  which  must  be  expended  on  the  electro- 
lyte to  overcome  the  chemical  affinity  of  the  ions.  In  ex- 
pending work  in  this  manner  on  the  electrolyte,  we  may  be 
said  to  add  intrinsic  energy  to  the  ions  :  after  being  decom- 
posed they  possess  a  potential  energy  in  virtue  of  which 
they  can  recombine,  and  during  the  recombination  they 
must  manifest  in  some  form  the  energy  given  them  when 
they  were  decomposed.  They  may  manifest  this  energy  in 
the  form  of  heat,  and  if  allowed  to  do  so,  the  total  amount 
of  this  heat  of  combination  must  be  equivalent  to  the  energy 
expended  in  decomposing  them.  Thus,  calling  6  the  heat 
produced  by  the  combination  of  a  unit  of  weight  of  one  ion 
with  the  other,  and  E  the  electro-chemical  equivalent  of  the 
first  ion,  then  de  will  be  the  heat  produced  during  the 
combination  of  as  much  of  that  ion  as  would  be  decom- 
posed by  the  unit  quantity  of  electricity,  and  j  6  e  will  be 
the  mechanical  equivalent  of  that  heat  where  j  is  41572500, 
being  Joule's  coefficient,  or  the  number  of  absolute  units 
of  work  equivalent  to  the  heat  which  will  raise  one  gramme 
of  water  one  degree  centigrade.  Thus  the  equation  ex- 
pressing the  equivalence  between  the  heat  resulting  from 
the  combination  of  two  ions,  and  the  work  done  in  decom- 
posing them,  will  be  — 


IQ  = 
or  i  =  j  6  £ 


This  equation  gives  the  value  of  the  electromotive  force  which 
is  absolutely  necessary  to  effect  the  decomposition.  If  we 
have  less  electromotive  force  than  this,  i  Q  can  never  equal 
Q  j  6  e  ;  or  the  work  done  by  the  current,  no  matter  what  the 
resistance  may  be,  can  never  be  sufficient  to  separate  the 
weight  Q  e  of  the  ion  from  its  electrolyte.  If  a  greater 
electromotive  force  than  this  be  maintained  between  the 
electrodes,  the  decomposition  will  proceed  very  rapidly,  but 


CHAP.  XI. J  Chemical  Theory  of  Electromotive  Force.  171 

since  I  Q  will  be  greater  than  Q  j  0  e,  some  of  the  energy  of 
the  current  will  be  spent  otherwise  than  in  decomposing 
the  electrolyte. 

§  7.  If  we  look  on  the  work  done  in  separating  two  ions 
as  a  product  of  two  factors,  one  factor  being  the  weight  of 
one  ion  M,  and  the  other  factor  the  chemical  affinity  E,  per 

unit  of  weight,  then  M  E  =  i  Q,  or  E  =  i  S, 

M 

But  the  ratio  -  is  equal  to  t ;  hence  E  =  i,  so  that  the  che- 
mical affinity  of  the  ions  per  electro-chemical  equivalent  is 
equal  to  the  electromotive  force  required  to  just  decompose 
the  electrolyte. 

§  8.  The  ions  which  by  their  combination  form  an  electro- 
lyte may  generate  a  current  instead  of  producing  heat.  If 
the  whole  energy  due  to  chemical  affinity  is  so  employed,  the 
value  of  the  energy  will,  as  before,  for  each  electro-chemical 
equivalent  e  be  the  product  j  0  s.  The  mechanical  equivalent 
of  the  current  produced  is  IIQI,  where  ^  and  QI  are  the 
electromotive  force  and  quantity  of  electricity  produced  by 
the  combination  of  the  ions  ;  but  the  electromotive  force 
just  required  to  decompose  the  ions  is  exactly  balanced  by 
the  E.  M.  F.  which  the  combination  of  the  ions  can  produce. 
In  other  words,  il  =  i,  and  therefore  QJ  =  Q.  Hence  the 
electromotive  force  due  to  the  combination  of  any  pair  of 
ions  is  equal  to  j  0  e  or  the  mechanical  equivalent  of  as  much 
of  the  chemical  action  as  goes  on  with  the  unit  of  the  current 
in  the  unit  of  time. 

e  may  be  taken  for  either  ion.  0  e  is  constant,  whichever 
is  taken. 

A  table  giving  the  values  of  6  is  required  before  we  can 
calculate  from  the  table  of  electro-chemical  equivalents  the 
E.  M.  F.  which  any  given  combination  will  produce. 

§  9.  When  a  series  of  chemical  actions  take  place  in  a 
circuit,  some  of  these  may  tend  to  produce  an  E.  M.  F.,  the 
others  to  resist  it.  We  express  this  fact  by  saying  that  the 


172  Electricity  and  Magnetism.          [CHAP.  XI. 

Respective  values  of  i  for  the  several  reactions  may  be  posi- 
tive or  negative.  The  resultant  value  or  actual  electromotive 
force  tending  to  produce  a  current,  or  to  resist  decomposi- 
tion, is  the  algebraic  sum  of  all  the  values  of  i.  Thus,  in 
the  galvanic  cefl  known  as  DanielPs  cell,  the  electrodes  are 
copper  and  zinc;  next  the  copper  there  is  a  saturated  solution 
of  sulphate  of  copper,  and  next  the  zinc  a  solution  of  sul- 
phate of  zinc.  The  chemical  action  is  as  follows  :  i.  The 
zinc  electrode  combines  with  oxygen.  2.  The  oxide  thus 
formed  combines  with  sulphuric  acid  and  forms  sulphate  of 
zinc.  3.  Oxide  of  copper  is  separated  from  the  sulphate. 
4.  The  copper  in  this  oxide  is  separated  from  the  oxygen. 

The  oxygen  of  the  water  is  separated  at  the  zinc  electrode 
from  the  hydrogen,  and  at  the  other  electrode  this  hydrogen 
recombines  with  the  oxygen  from  the  oxide  of  copper, 
but  this  alternate  decomposition  and  recombination  of  the 
elements  of  water  can  neither  increase  nor  decrease  the 
E.  M.  F.  of  the  cell,  the  actions  being  opposite  and  equal. 

1.  The  heat  evolved  by  the  combination  of  one  gramme  of 
zinc  with  oxygen  is  1,301  units. 

2.  The  heat  evolved  by  the  combination  of  the  1*246 
gramme  of  oxide  thus  formed  with  dilute  sulphuric  acid  is  369 
units. 

3.  The  heat  evolved  by  the  combination  of  the  equivalent 
quantity  "9727  of  a  gramme  of  copper  with  oxygen  is  588*6 
units. 

4.  The  heat  evolved  by  the  combination  of  1*221  gramme 
of  the  oxide  thus  formed  with  dilute  sulphuric  acid  is  293 
units. 

The  thermal  equivalent  of  the  whole  chemical  action  due 
to  one  gramme  of  zinc  is  therefore  1301  -f  369  —  (588*6  + 
293)  =  788*4;  but  we  require  the  thermal  equivalent  of  a. 
weight  of  zinc  equal  to  f,  and  this  we  obtain  by  multiplying 
788*4  into  '00342,  giving  for  0  e  the  value  2*696  ;  next,  to 
obtain  the  value  of  i,  this  product  is  multiplied  by  j  or 
41572500,  and  we  then  obtain  for  the  electromotive  force  of 


CHAP.  XL]  Chemical  Theory  of  Electromotive  Force.  173 

a  DanielPs  cell  about  112,000,000  units,  a  value  which 
agrees  closely  with  the  result  of  direct  experiment.  This 
theory  and  example  are  taken  from  Sir  W.  Thomson's 
paper  in  the  '  Philosophical  Magazine'  for  1851. 

§  10.  The  separation  of  substances  into  ions  which  appear 
separately  at  the  two  electrodes  is  a  fact  made  useful  in 
many  ways.  The  elements  or  elementary  groups  gather 
at  the  electrodes  in  a  state  of  great  purity,  and  hence 
the  process  of  electrolysation  is  made  use  of  to  obtain 
pure  chemicals.  Metals  may  be  deposited  in  this  way  on  an 
electrode  of  any  form  which  it  is  desired  to  copy.  The 
metal  copy  thus  formed  is  called  an  electrotype.  The  nobler 
metals  are  often  deposited  on  electrodes  of  baser  materials 
for  the  sake  of  ornament.  These  electrodes  are  then  said  to 
be  electro-plated  with  the  nobler  metals.  Some  substances 
can  only  be  decomposed  by  electrolysis,  and  some  ions 
can  only  be  maintained  in  a  state  of  separation  while  the 
current  is  passing. 

§11.  The  passage  of  an  ion  from  the  place  where  it  is 
first  decomposed  to  the  electrode  appears  to  take  place  by 
a  series  of  combinations  and  decompositions.  Thus,  when  a 
molecule  of  water  half-way  between  the  electrodes  is  decom- 
posed, neither  the  hydrogen  nor  oxygen  cross  the  water  as 

FIG.  84. 

r 


free  gases,  but  the  hydrogen  of  d,  shown  by  the  white  half  of 
the  molecule,  Fig.  84,  combines  with  the  oxygen  of  c,  shown 
by  the  black  half  of  that  molecule.  This  sets  the  hydrogen 
of  c  free  to  combine  with  the  oxygen  of  b,  and  finally 
the  hydrogen  of  b  combines  with  the  oxygen  of  #,  leav- 
ing the  hydrogen  of  a  free  at  the  negative  electrode.  A 
similar  series  of  compositions  and  decompositions  leaves  the 


1 74  Electricity  and  Magnetism.          [CHAP.  XI. 

oxygen  of  g  free  at  the  positive  electrode.  This  is  shown 
by  the  fact  that  ions  can  be  transmitted  through  materials 
for  which  they  have  a  strong  chemical  affinity  without  com- 
bining with  them. 

FIG.  85. 


Thus,  put  a  solution  of  sulphate  of  sodium  into  A,  Fig.  85  ; 
dilute  syrup  of  violets  into  B,  and  pure  water  into  c ;  pass  a 
current  from  an  electrode  in  c  to  an  electrode  in  A.  The 
sulphate  in  the  vessel  A  will  be  decomposed.  Soda  will  be 
found  in  A,  and  sulphuric  acid,  which  must  have  come  from 
A,  will  be  found  in  c.  Nevertheless,  the  colour  of  the  solu- 
tion in  B  will  not  have  been  altered ;  whereas  the  addition 
of  a  very  small  quantity  of  free  acid  to  B  will  produce  a  dis- 
tinct red  colour. 


CHAPTER  XII. 

THERMO-ELECTRICITY. 

§  1.  WHEN  the  junctions  of  a  circuit  made  of  two  metals 
are  at  different  temperatures,  a  current  of  electricity  gene- 
rally flows  through  the  circuit.  The  electromotive  force 
producing  this  current  depends,  i,  on  the  metals  employed; 
2,  on  the  difference  of  temperature  between  the  junctions; 
and,  3,  on  the  mean  temperature  of  the  junctions. 

When  the  mean  temperature  of  the  junctions  is  kept  the 
same  for  circuits  containing  pairs  of  metals  in  various  com- 
binations, and  when  the  difference  of  temperatures  between 
the  junctions  is  small  and  constant,  the  electromotive 


CHAP.  XII.]  Thermo- Electricity.  175 

force  of  each  circuit  depends  only  on  the  metals  employed. 
Let  us  call  6  (A  B)  the  numerical  factor  by  which  the 
difference  of  temperature  r  between  the  junctions  must  be 
multiplied  to  give  the  E.  M.  F.  of  a  circuit  composed  of  two 
metals  A  and-B  at  the  mean  temperature  /,  and  let  us  call  the 
value  of  this  numerical  factor,  when  T  is  equal  to  unity,  the 
thermo-electric  power  of  the  circuit  A  B  at  the  temperature  /. 
Then,  calling  </>  (A  c)  and  ^  (B  c)  the  thermo-electric  powers 
of  the  pair  A  and  c  and  of  the  pair  B  and  c,  we  find  experi- 
mentally that  <£>  (B  c)  =  <j>  (A  c)  —  <?>(A  B).  This  equation  ex- 
presses the  fact  that  the  thermo-electric  power  of  any  pair  of 
metals  is  equal  to  the  difference  between  the  thermo-electric 
powers  of  those  metals  relatively  to  some  one  standard 
metal  A.  In  order  therefore  to  calculate  the  thermo-electric 
power  of  any  pair  of  metals  it  is  sufficient  that  we  determine 
experimentally  the  thermo-electric  power  of  all  metals 
relatively  to  some  one  metal  used  as  a  standard.  In  what 
follows  lead  will  be  taken  as  the  standard  metal. 

§  2.  We  call  a  metal  thermo-electrically  positive  to 
another,  when  the  E.  M.  F.  in  a  circuit  of  these  two  metals 
sends  a  current  from  the  first  to  the  second  across  the 
hot  junction  \  the  difference  of  temperatures  T  being  sup- 
posed small.  It  follows  from  §  i  that  the  metals  mayjfor 
any  one  mean  temperature  t  be  arranged  in  a  series  such 
that  each  will  be  positive  relatively  to  that  beneath  it;  it 
follows,  moreover,  that  a  number  may  be  assigned  to  each 
metal  proportional  to  its  thermo-electric  power  relatively, 
say,  to  lead,  and  such  that  the  algebraic  difference  be- 
tween these  numbers  for  any  two  metals  will  express  in  any 
arbitrary  units  the  E.  M.  F.  of  a  circuit  of  those  two  metals 
when  the  junctions  are  at  the  mean  temperature  /,  but  differ 
by  a  small  constant  difference  r  or,  say,  by  unity.  The 
thermo-electric  series  printed  in  most  books  give  approxi- 
mately numbers  of  this  kind,  but  the  experiments  on  which 
they  are  based  have  generally  been  conducted  without 
reference  to  the  condition  that  the  mean  temperature  / 


1 76 


Electricity  and  Magnetism.        [CHAP.  XII. 


should  be  constant,  and  this  temperature  is  seldom  given. 
The  thermo-electric  series  differs  entirely  at  different  tem- 
peratures. The  following  is  compiled  from  Dr.  Matthies- 
sen's  experiments,  and  is  such  that  approximately  the  ther- 
mo-electric power  relatively  to  lead  is  expressed  in  microvolts 
per  degree  Centigrade. 

Pressed  Antimony  wire  —     2 -8 
Silver  pure  hard          .    —     3 
Zinc  pure  pressed        .    —    3*7 
Copper   galvanoplasti  - 

cally  precipitated     .    —    3-8 
Antimony  commercial 

pressed  wire  .         .    —     6 
Arsenic      .         .         .    —  13*56 
Iron  pianoforte  wire  .    —  17 '5 
Antimony  axial  .   —  22 -6 

Antimony  equatorial  .  -  26*4 
Red  Phosphorus  .  —  29  7 
Tellurium  .  .  —  5°2 

Selenium  .         ..  —    807 


The   mean   temperature    for  which   these    numbers   are 
approximately  true  may  be  taken  at  from  19°  to  20°  Centi 
grade. 

§  3.  Any  two  metals  joined  by  a  third  metal  so  as  to  form  a 
circuit  have  an  E.  M.  F.  equal  to  that  which  they  would  have 
had  if  directly  joined,  provided  both  junctions  with  the  third 
metal  are  at  one  temperature ;  thus  in  Fig.  86  the  three 
circuits  all  have  the  same  E.  M.  F. — that  due  to  zinc  and 
antimony  alone.  The  copper  wire  might  be  replaced  by 
any  complex  arrangement  of  substances  without  interfering 
with  the  E.  M.  F.  of  the  circuit,  provided  the  junctions 
were  all  at  one  temperature,  except  those  intended  to  be 
effective.  Thus  the  E.  M.  F.  of  a  thermo-electric  pair — such  as 
zinc  and  antimony — may  be  tested  by  observing  the  current 
flowing  through  a  complex  circuit  composed,  for  instance, 
of  the  copper  wire  of  a  galvanometer  having  brass  terminals. 


Bismuth    pressed    com- 

mercial wire     . 

+  97 

Bismuth    pure    pressed 

wire 

89 

Bismuth  crystal  axial     . 

65 

Bismuth    crystal    equa- 

torial 

45 

Cobalt 

22 

Argentine    . 

"75 

Quicksilver 

•418 

Lead  .... 

0 

Tin      .         . 

—         *  I 

Copper  of  commerce     . 

—     -i 

Platinum      . 

-     '9 

Gold   . 

—    I  '2 

CHAP.  XII.] 


Thermo-Electricity. 


177 


and  of  German  silver  resistance  coils.  We  must,  however,  in 
such  cases  test  the  equality  of  the  temperatures  at  the  other 
junctions  by  observing  whether  any  current  is  produced 
when  the  thermo-electric  element  is  removed,  and  the 
copper,  brass,  and  German  silver  connections  joined  so  as 
to  make  an  independent  circuit  exactly  similar  to  that 
previously  used  except  as  regards  the  removal  of  the  zinc 
and  antimony,  or  other  thermo-electric  pair. 

FIG.  86. 


Gold 


§  4.  The  thermo-electric  powers  of  different  combinations 
not  only  change  with  a  change  of  mean  temperature,  but 
they  change  in  very  different  proportions.  Thus  the 
thermo-electric  power  of  copper-silver  differs  little  for  tem- 
peratures between  o°  and  100°,  but  the  thermo-electric 
power  of  iron-copper  varies  rapidly ;  so  rapidly,  indeed, 
as  to  fall  to  zero  at  about  230°,  and  then  again  to  increase, 
but  with  the  opposite  sign ;  so  that  whereas  copper  is  posi- 
tive to  iron  below  230°,  it  is  negative  to  iron  above  that 
temperature.  It  follows  that,  if  we  are  to  possess  accurate 
knowledge  as  to  the  thermo-electric  relations  of  metals  over 
a  considerable  range  of  temperatures,  we  must  have  suffi- 
cient knowledge  to  construct  such  a  diagram  as  is  shown  in 
Fig.  87,  where  the  vertical  ordinates  indicate  temperatures 
in  degrees  Centigrade,  and  the  horizontal  ordinates  the 
thermo-electric  powers  in  microvolts  of  the  metals  relatively 
to  lead. 


CHAP.  XII.]  Thermo- Electricity.  179 

This  diagram  may  be  looked  upon  as  simply  one  mode  of 
tabulating  the  thermo-electric  powers  of  metals  relatively  to 
one  another  at  different  temperatures,  the  horizontal  scale 
being  so  arranged  that  the  distance  between  the  two  lines  of 
any  given  metals  at  any  temperature  gives  the  thermo- 
electric power  of  the  two  metals  at  that  temperature.* 

Thus  the  thermo-electric  power  of  copper  and  iron  at  50° 
is  nearly  11*4,  and  at  260°  is  zero,  and  at  400°  it  is  —7*6.  I 
here  call  the  thermo-electric  power  +  when  the  current  is 
from  the  first-named  to  the  second-named  of  a  thermo- 
electric pair  across  the  hot  junction. 

§  5.  For  any  very  small  differences  of  temperature  the 
electromotive  force  of  a  pair  is  equal  to  the  product  of  the 
difference  of  temperature  between  the  junctions  into  the 
thermo-electric  power,  so  that  the  area  of  a  narrow  strip 
(approximately  a  parallelogram)  represents  this  E.  M.  F.  on 
the  diagram.  When  the  breadth  of  this  strip  is  unity,  or  the 
difference  of  temperature  i°,  the  electromotive  force  is 
simply  equal  to  the  ordinate  or  to  the  thermo-electric  power. 
When  the  difference  of  temperatures  is  considerable — say  50° 
— the  electromotive  force  is  the  same  as  if  we  had  5  pairs  of 
junctions  arranged  as  in  Fig.  88 ;  thus  if  while  a  a}  were 


FIG.  88. 

80°    a 

•Pill ''rga         Hillli iillHil         illillillk 


50°   60°   60°  70°   70°  80°   80°   go9   90°  100°  ioo( 

iliimilllf~ 


i      iiiiiiiiiiii     ilium — iiiii — iiiir 

5o9  50°   60°   60°   70°   70°   80°   80°   90°   90°   ioo 

joined  we  were  to  complete  a  circuit  by  joining  the  junctions 
b  b^  we  should  in  this  circuit  have  an  electromotive  force 
equal  to  the  parallelogram  ##!.  in  Fig.  89,  where  M  N  and  o  P 
represent  the  thermo-electric  lines  for  copper  and  iron. 

*  The  first  diagram  of  this  kind  was  given  by  Sir  William  Thomson 
in  the  Bakerian  Lecture  on  the  electro-dynamic  qualities  of  metals,  "PhiL 
Trans.  1856,  p.  708. 

N2 


180  Electricity  and  Magnetism.       [CHAP.  XI T. 

If  we  now  were  to  break  the  circuit  at  a  alt  Fig.  88,  and 
leaving  b  b\  joined  were  to  join  cc\,  we  should  have  a  circuit 
b'b\  cl  c,  in  which  the  E.  M.  F.  would  be  represented  in  Fig.  89 
by  the  parallelogram  bbv  Similarly  in  the  circuit  dd\  cc^ 
Fig.  88,  the  E.  M.  F.  would  be  represented  by  the  area  c  c^  in 
Fig.  89,  &c. 

FIG.  89. 


Now  when  a  a{  are  joined,  and//!  are  joined,  and  all  the 
other  cross  connections  broken,  the  E.  M.  F.  of  the  series  is 
the  sum  of  all  the  electromotive  forces  of  each  of  the  little 
circuits  a  al  b  b^b  blc  c^  c  cl  d  d\,  &c.,  and  is  consequently 
represented  by  the  area  A  A!  F!  F  in  Fig.  89.  Thus  the 
electromotive  force  of  any  pair  with  the  two  junctions  at  any 
two  temperatures  can  be  calculated  by  calculating  the  area 
enclosed  between  the  two  thermo-electric  lines  of  those 
metals,  and  the  ordinates  corresponding  to  the  two  extreme 
temperatures. 

§  6.  In  taking  out  this  area  we  must,  however,  observe 
that  if  the  areas  to  the  left  of  any  point  where  two  lines  cut 
are  called  positive,  those  to  the  right  must  be  termed  nega- 
tive, for  they  represent  an  E.  M.  F.  tending  to  send  the  current 
in  the  reverse  direction.  If,  therefore,  the  two  junctions  are 


CHAP.  XII.]  TJiermo-Electricity.  181 

at  such  temperatures  that  the  areas  are  equal,  no  E.  M.  F. 
will  be  produced  in  the  circuit. 

The  points  where  the  two  lines  for  any  metals  cut  are 
called  the  neutral  points  for  those  metals,  because  at  that 
temperature  the  metals  are  neither  positive  nor  negative  re- 
latively to  one  another,  their  thermo-electric  powers  being 
equal.  When  the  lower  junction  is  so  far  from  the  neutral 
point  that  the  triangular  area  intercepted  by  the  ordinate  of 
its  temperature  is  greater  than  the  triangular  area  cut  off  by 
the  ordinate  of  the  higher  temperature,  the  current  will  go 
from  the  metal  highest  on  the  scale  below  the  neutral  point 
to  the  other  through  the  hot  junction.  The  direction  of  the 
current  will  be  the  opposite  if  the  triangular  area  above  the 
neutral  point  is  the  greatest 

§  7.  So  far,  we  have  been  following  Sir  William  Thomson. 
Professor  Tait,  led  by  theoretical  considerations,  has  experi- 
mentally proved  that  the  thermo-electric  lines  are  in  most  cases 
approximately  straight  between  o°  and  300°  Centigrade,  and 
probably  at  much  higher  temperatures.  This  greatly  facilitates 
the  calculation  of  E.  M.  F.,  because  the  areas  to  be  dealt  with 
are  simply  triangles,  or  trapezes.  Let  m  be  the  distance  sepa- 
rating the  lines  of  the  two  metals  forming  the  pair  at  the  mean 
temperature  of  the  junctions ;  let  tl  —  t,2  be  the  difference 
of  temperatures  :  then  m  (tx  —  /2)  is  the  E.  M.  F.  of  the 
pair  under  those  conditions,  being  the  area  of  the  trapeze, 
or  triangle,  above  described.  It  follows  from  the  above, 
that  when  the  mean  temperature  of  the  two  junctions  is 
that  of  the  neutral  point,  no  current  will  flow  through  the 
circuit.  This  gives  a  means  of  determining  the  neutral 
points  of  metals  with  great  accuracy.  Professor  Tait  has 
also  established  the  curious  fact  that  the  thermo-electric 
line  of  iron,  whether  pure  or  commercial,  when  prolonged 
towards  red  heat,  is  a  sinuous  or  broken  straight  line,  so  that 
there  may  be  two  or  more  neutral  points  in  one  circuit  when 
iron  or  steel  is  one  of  the  two  metals. 

The  E,  M.  F.  of  any  pair  may  be  calculated  in  microvolts 


182 


Electricity  and  Magnetism.       [CHAP.  xn. 


from  the  diagram  (Fig.  87),  taking  the  measurement  of  the 
mean  distance  between  the  lines  of  the  metals  by  the  hori- 
zontal scale,  and  the  vertical  measurements  in  degrees 
Centigrade ;  but  it  is  obviously  more  convenient  to  calculate 
than  to  measure  the  length  of  the  mean  distance  between 
the  lines,  and  for  this  purpose  the  following  table  is  given, 
containing  the  tangents  of  the  angles  at  which  the  lines  are 
inclined.  Let  k\  and  £2  be  the  tangents  for  two  given 

Prof.  Taifs  Thermo-electric  Table  (converted  to  give  E.M.F.  in  microvolts). 


Metals. 

Neutral  Point  with 
Lead. 
Degrees  Centigrade. 
« 

Tangent  of  Angle  with  ' 
Lead  Line. 
k 

Cadmium     . 

-69 

-  -0364 

Zinc    . 

-32 

-  -0289 

Silver 

-  "5 

—  '0146 

Copper 

-68 

—  -0124 

Brass 

+  27 

—  -0056 

Lead  . 



Aluminium 

-JI3 

+  -0026 

Tin     . 

+  45 

+  -0067 

German  silver 
Palladium    . 

-3H 
-181 

+  -0251 
4-  '0311 

Iron    . 

+  357 

+  -0420 

Note. — The  straightness  of  the  thermo-electric  lines  has  not  been 
verified  below  o° ;  hence  the  table  must  only  be  used  to  calculate 
E.  M.  F.  for  couples  between  o°  and  400°  or  500°  Centigrade. 

The  metals  used  were  not  chemically  pure. 

This  table  is  calculated  from  the  iron  series  in  Prof.  Tait's  table, 
p.  599.  Proc.  R.S.E.  1871-72,  taking  the  E.M.F.  of  a  Grove's  cell 
as  I  -93  volts. 

metals.  Let  nl  and  ;/2  be  the  temperatures  of  their  neutral 
points  with  lead.  Let  tm  be  the  mean  temperature  of  the 
junctions ;  then  the  mean  ordinate  or  m  is  given  by  the 
formula 

m  =  /&!  («!  -  Q  -  £2  («2  -  Q 

Thus,  let  the  mean  temperature  of  a  pair  of  copper-iron 
junctions  be  50°,  and  the  difference  of  the  temperatures  of 
the  junctions  100°;  then  (50  +  68)  (  —  -0124)  =  —  1-46  is 


CHAP.  XII.]  Thermo-Electricity.  183 

one  portion  of  the  mean  ordinate  (for  copper),  and 
(50  —  357)  ('042)  =  —  12-9  is  the  other  (for  iron). 
Their  difference  is  11*43,  an^  tm's  multiplied  into  100°  gives 
1143  as  the  E.  M.  F.  of  the  copper-iron  pair  in  microvolts. 
When  the  thermo-electric  lines  of  two  metals  are  nearly 
parallel,  the  E.  M.  F.  produced  by  a  pair  of  those  metals  will 
be  nearly  proportional  to  the  difference  of  temperatures 
maintained  between  their  junctions.  For  metals  or  alloys, 
the  lines  of  which  diverge,  no  such  law  even  approximately 
holds  good,  and  it  is  necessary,  before  the  E.  M.  F.  can  be  cal- 
culated, that  we  should  know  not  only  the  difference  of  tem- 
peratures, but  the  actual  temperatures  of  the  junctions. 

§  8.  A  number  of  thermo-electric  pairs,  or  elements,  may  be 
joined  in  series,  so  as  to  give  an  E.  M.  F.  which  is  the  sum  of 
the  electromotive  forces  of  all  FIG.  9o. 

the  elements.     To  do  this  it 
is  only  necessary  to  join  the 
metals,  as  shown  in  Fig.  90,  and 
keep  all  the  junctions  on  one 
side,  as  at  A,  warm  while  the  ^ 
other  side  is  cold.    .Batteries^' 
of  this  kind  are  easily  made 
with  exceedingly  small  resist- 
ance, so  that  when  the  other 

resistances  in  the  circuit  are  also  small,  considerable  currents 
will  be  produced — greater  currents  than  could  be  obtained 
under  similar  circumstances  from  a  Daniell's  cell  of  moderate 
size.  A  bismuth-antimony  pair  may  be  prepared  having,  say, 
an  E.  M.  F.  of  100,000  microvolts,  or  about  -^  the  E.  M.  F.  of  a 
Daniell's  cell,  while  the  resistance  might  be  reduced  to  almost 
any  desired  extent  by  increasing  the  section  of  each  element. 
Thus,  if  each  element  were  about  2  centimetres  in  length, 
and  a  tenth  of  a  square  centimetre  in  section,  the  resistance 
of  the  pair  would  be  about  3,370  microhms,  and  the  resist- 
ance of  100  such  pairs  would  be  337,000  microhms,  or 
'337  ohm,  so  that  through  a  short  circuit  they  would  give 


1 84 


Electricity  and  Magnetism.       [CHAP.  XII. 


£  greater  current  than  any  except  the  largest  sized  Daniell's 
cell.  There  are  thermo-electric  pairs  which  give  a  much 
greater  E.  M.  F.  than  the  above,  but  generally  the  increase  in 
E.  M.  F.  is  to  a  great  extent  counterbalanced  by  an  increase  in 
the  internal  resistance  of  the  pair. 

§  9.  Thermo-electric  currents  are  produced  by  non-metallic 
substances.  Metals  and  fusible  salts  form  powerful  pairs, 
which  are  generally  held  to  be  thermo-electric,  and  Becquerel 
has  constructed  a  battery  of  the  artificial  sulphuret  of  copper 
and  German  silver,  in  which  the  salt  is  used  without  being 
fused. 

Thermo-electric  currents  are  also  produced  in  circuits  of 
metals  and  liquids,  and  probably  in  simple  liquid  circuits. 

§  10.  The  chief  practical  use  to  which  thermo-electric  bat- 
teries have  been  put  is  the  measurement  of  small  differences 
of  temperature.  Melloni  introduced  this  method  of  ob- 
serving changes  of  temperature.  A  thermo-electric  battery, 
Figc  91,  is  connected  by  the  terminals  /  ^  with  a  galvano- 

FIG.  91. 


meter  having  a  very  small  resistance;  one  series  of  junctions 
u  is  maintained  at  one  temperature  as  nearly  as  possible, 
being  enclosed  in  a  metal  case ;  the  other  series  of  June- 
tions  A  is  exposed  to  radiation  from  the  objects  the  tem- 
peratures of  which  are  to  be  compared.  The  junctions  are 


CHAP.  XII.]  Thermo-Electricity.  185 

screened  by  tubes  from  the  radiation  of  other  objects  ; 
these  tubes  are  shown  removed  from  the  battery  in  Fig.  91. 

When  any  substance  warmer  than  the  space  opposite  B  is 
allowed  to  radiate  heat  upon  the  junctions  A,  the  galvanometer 
is  immediately  deflected.  When  the  junctions  A  radiate  heat 
to  a  colder  substance  than  B,  so  as  to  become  colder  than 
B,  a  deflection  to  the  opposite  side  is  produced  ;  for  small 
differences  of  temperature  the  currents  produced  are  pro- 
portional to  the  differences  of  temperature.  This  arrange- 
ment is  so  sensitive,  that  by  its  aid  the  heat  radiated  by 
the  fixed  stars  has  been  detected. 

§  11.  In  accordance  with  the  doctrine  of  the  conservation 
of  energy,  heat  is  transformed  into  electricity  in  the  thermo- 
electric circuit ;  the  work  done  by  the  current  is  precisely 
the  equivalent  of  the  heat  so  transformed.  If  the  whole 
work  of  the  current  consists  in  heating  the  conductors,  the 
effect  is  merely  a  transference  of  heat  by  means  of  elec- 
tricity from  one  part  of  the  circuit  to  another ;  so  that,  in 
accordance  with  the  law  of  dissipation  of  energy,  the  parts  of 
the  circuit  are,  on  the  whole,  more  nearly  at  one  tempera- 
ture than  if  no  current  had  been  produced,  and  heat  had 
merely  been  conducted  along  the  wires.  If  the  current  is 
employed  to  do  mechanical  work,  an  equivalent  amount  of 
heat  is  abstracted  from  the  circuit,  and  reappears  in  the 
bearings  of  the  working  machine  and  the  materials  it  works 
upon  ;  similarly  a  portion  of  the  work  done  may  be  electro- 
chemical. In  whatever  form  the  work  is  done,  in  the  whole 
circuit  this  work  will  be  equal  to  I  Q  §  2,  Chap.  VIII. 

The  heat  is  transformed  into  electricity  at  the  hot  junction, 
and  also  at  unequally-heated  portions  of  one  or  both  metals. 
Peltier  discovered  that  a  current  flowing  through  a  circuit  of 
two  metals  heated  one  junction  and  cooled  the  other.  Now, 
the  current  which  flows  in  a  thermo-electric  circuit  flows  in 
such  a  direction  in  general  as  to  heat  the  cold  junction  and 
cool  the  hot  one ;  so  that  for  some  time  it  was  considered 
that  the  heat  producing  the  current  was  wholly  absorbed  at 


1 86  Electricity  and  Magnetism.       [CHAP.  XII. 

the  hot  junction,  and  given  out  at  the  cold  junction  dimin- 
ished by  radiation,  and  by  an  amount  equivalent  to  the  work 
done  in  the  rest  of  the  circuit. 

Sir  William  Thomson  pointed  out  that  this  explanation 
was  incomplete,  for  when  a  junction  is  at  the  neutral  point 
no  Peltier  effect  can  occur  ;  the  two  metals  are  then  thermo- 
electrically  identical;  nevertheless  when  the  hot  junction  is  at 
the  neutral  point  and  the  other  junction  at  a  lower  tem- 
perature, a  current  is  observed,  increasing  as  the  tempera- 
ture of  the  lower  junction  is  diminished,  and  the  direc- 
tion of  the  current  is  such  as  to  heat  the  cold  junction. 
Heat  must  therefore  be  absorbed  at  other  parts  of  the 
circuit  than  at  either  junction. 

§  12.  We  may,  perhaps,  best  conceive  of  the  manner  in 
which  this  heat  is  absorbed  by  considering  what  would  occur 
if  a  current  were  passed  through  a  series  of  metal  pieces, 
arranged  as  in  Fig.  92,  where  each  is  in  succession  more  posi- 
tive than  that  which  precedes  it,  a  being  the  least  and  k  the 
most  positive.  If  a  current  is  passed  from  a  to  k,  it  will  flow 
in  the  direction  opposed  to  that  in  which  a  current  would 

FIG.  92. 
abedefffhtjk 


J I 


flow  across  any  of  the  junctions,  if  that  were  the  hot  junction 
of  a  circuit  made  of  those  two  metals,  and  therefore  every 
junction  would  be  heated ;  whereas  if  the  current  were 
passed  in  the  other  direction,  as  shown  by  the  arrow,  every 
junction  would  be  cooled.  If  the  Peltier  effect  at  every 
junction  were  the  same,  the  bar  would  be  heated  and  cooled 
uniformly  ;  but  if  the  Peltier  effect  increased  from  a  towards 
k,  then  the  bar  would  be  unequally  heated  or  cooled  by  the 
passage  of  the  current.  The  current  in  the  direction  of  the 
arrow  would  cool  the  bar  most  near  k  so  as  apparently 
to  heap  up  heat  towards  a,  whereas  a  current  in  the  opposite 


CHAP.  XIII.]  Galvanometers.  187 

direction  would  heap  up  heat  towards  k  •  in  other  words, 
in  such  a  bar  as  this,  positive  electricity  might  be  said  to 
carry  heat  with  it.  Now,  a  copper  bar,  or  wire,  with  the  end 
k  cooler  than  the  end  a,  behaves  as  if  it  were  composed  of 
an  infinite  number  of  such  little  elements  ;  a  current  from 
hot  to  cold  heats  it  and  carries  heat  with  it ;  whereas  an 
iron  bar  behaves  as  if  when  the  end  k  were  the  hotter  it 
were  the  more  positive,  so  that  a  current  from  cold  to 
hot  heats  iron.  The  heaping  up  of  heat  in  iron  goes  in 
the  direction  opposed  to  that  of  the  current.  We  see  that 
a  current  from  hot  to  cold  in  iron  absorbs  heat,  and  one 
from  cold  to  hot  absorbs  heat  in  copper ;  and.  hence,  when  a 
pair  is  formed  of  copper  and  iron  with  its  hotter  junction 
at  the  neutral  point,  the  current  goes  from  cold  to  hot  in 
the  copper  and  hot  to  cold  in  the  iron.  Hence  the  copper 
and  iron  both  absorb  heat,  and  the  electromotive  forces  of 
the  two  are  added.  With  most  pairs  of  metals  the  E.  M.  F. 
in  the  one  unequally  heated  metal  is  opposed  to  that  in  the 
other.  In  this  case  the  stronger  E.  M.  F.  overcomes  the 
weaker,  and  the  resultant  current  is  due  to  the  difference  of 
electromotive  forces.  The  discovery  of  the  absorption  or 
evolution  of  heat  due  to  the  unequal  temperatures  of  metals 
and  its  convection  were  predicted  from  theoretical  conside- 
rations by  Sir  William  Thomson,  who  afterwards  verified  his 
conclusions  by  experiment. 


/ 

I 


CHAPTER  XIII. 

GALVANOMETERS. 


§  1.  A  GALVANOMETER  is  an  instrument  intended  to  detect 
the  presence  of  a  current  and  measure  its  magnitude  ;  all 
forms  of  the  instrument  consist  of  a  coil  of  insulated  wire  and 
a  magnet  freely  hung  or  pivoted  so  as  to  be  easily  deflected 
by  the  passage  of  a  current  through  the  coil.  The  wire 
forming  the  coil  is  so  wound  that  each  turn  lies  in  a  plane 
approximately  perpendicular  to  the  axis  of  the  undeflected 


1 88  Electricity  and  Magnetism.     [CHAP.  XIII. 

magnet.  The  current,  in  passing  through  the  coil,  or  bobbin, 
of  insulated  wire,  produces  a  magnetic  field  in  the  space  in 
which  the  magnet  hangs,  and  the  couple  tending  to  deflect  the 
magnet  is  directly  proportional  to  the  strength  of  this  field 
and  to  the  moment  of  the  magnet.  The  opposing  couple 
tending  to  bring  back  the  magnet  to  its  undeflected  position 
may  be  due  to  various  causes. 

In  one  class  of  galvanometers  the  magnet  is  suspended 
or  supported  in  a  horizontal  plane,  and  the  opposing  couple 
is  simply  due  to  the  earth's  magnetism.  In  instruments  of 
this  class,  no  increase  in  the  moment  of  the  suspended 
magnet  will  increase  the  sensibility  of  the  instrument — that 
is  to  say,  it  will  not  increase  the  deflection  due  to  a  given 
current — for  by  just  as  much  as  the  deflecting  couple  is  in- 
creased, by  so  much  is  the  opposing  couple  also  increased. 
The  complete  magnetisation  of  the  needle  therefore  is 
not  of  much  consequence,  and  a  change  in  the  magneti- 
sation of  the  needle  does  not  alter  the  sensibility.  A 
small,  light  magnet  will  also  in  this  class  of  instruments  be 
deflected  through  the  same  angle  as  a  large,  heavy  one,  and 
will  have  the  following  advantages  :  ist.  That  the  small 
magnet  will  require  only  a  small  coil  to  surround  it,  and  that 
this  small  coil  will  for  the  same  number  of  turns  produce  a 
more  intense  magnetic  field  (§  8,  Chap.  VIII.)  than  the 
large  one,  and  offer  much  less  resistance  than  the  large 
coil,  if  made  of  the  same  wire.  2nd.  That  the  inertia  of  the 
small  magnet  being  less  relatively  to  the  magnetic  moment, 
it  will  reach  its  maximum  deflection  more  quickly,  and  will 
come  to  rest  more  rapidly  than  the  large  magnet.  It  will 
also  indicate  transient  currents  which  do  not  last  long 
enough  to  deflect  the  large  magnet. 

§  2.  In  a  second  class  of  galvanometers,  the  couple  oppos- 
ing the  deflection  is  due  not  to  magnetism,  but  to  weight. 
The  magnet  is  pivoted  in  a  vertical  plane,  and  has  one  end 
slightly  weighted,  so  as  to  hang  upright  when  undeflected. 
In  these  instruments  any  increase  in  the  magnetic  moment 


CHAP.  XIIL]  Galvanometers.  189 

of  the  magnet  increases  the  sensibility,  assuming  the  counter- 
balance or  directing  weight  to  remain  constant.  Hence  in 
these  instruments,  to  ensure  the  greatest  sensibility  the 
needles  should  be  magnetised  to  saturation,  but,  in  order 
to  ensure  constant  sensibility,  the  magnetism  of  the  needle 
must  remain  constant,  and  these  two  conditions  can  rarely 
oe  realised  together.  The  vertical  component  of  the 
earth's  magnetism  exerts  a  certain  directing  force  on  the 
needles,  but  its  effect  is  usually  nearly  insensible  in  com- 
parison with  that  of  the  weight.  These  instruments  are  not 
generally  intended  for  the  indication  of  such  small  currents 
as  those  described  in  §  i.  With  very  small  magnets  it  is 
difficult  to  diminish  the  friction  of  the  pivots  and  the  counter- 
balance proportionately  to  the  diminution  of  the  magnetic 
moment.  Hence  in  some  forms  of  the  second  class  it  may 
be  disadvantageous  to  dimmish  the  size  of  the  needle. 

§  3.  In  choosing  a  galvanometer  for  any  special  purpose, 
we  must  first  consider  the  character  of  the  circuit  into  which 
it  is  to  be  introduced.  The  introduction  of  the  coil  of  the 
galvanometer  into  the  circuit  will  in  all  cases  increase  the  re- 
sistance of  the  circuit,  and  therefore  diminish  the  current.  If 
the  coil  has  a  small  resistance  relatively  to  that  of  the  other 
portions  of  the  circuit,  the  diminution  of  the  current  will  be 
small,  and  may  in  some  cases  be  altogether  neglected ;  but 
if  the  resistance  of  the  original  circuit  be  small,  the  mere 
introduction  of  the  galvanometer  intended  to  measure  or 
indicate  the  current  may  reduce  that  current  a  thousandfold 
or  more.  In  all  cases  there  is  some  advantage  in  using  a 
galvanometer  coil  of  small  resistance,  but  in  order  that  a 
small  current  may  produce  a  sensible  magnetic  field,  it  is 
desirable  that  it  be  led  round  the  coil  as  often  as  possible,  a 
condition  antagonistic  to  the  former.  We  can  readily  see 
that  for  circuits  of  small  resistance  the  galvanometer  giving 
the  largest  deflection  will  be  an  instrument  having  a  coil 
with  few  turns  of  thick  wire;  but  for  circuits  of  large  resistance, 
galvanometers  having  thousands  of  turns  of  thin  wire  will  be 


Electricity  and  Magnetism.     [CHAP.  XIII. 

on  the  whole  most  advantageous.  In  some  writings  these 
two  classes  of  instruments  are  spoken  of  as  adapted  to  two 
different  classes  of  currents  instead  of  to  two  different 
classes  of  circuits.  The  instrument  with  numerous  turns  of 
fine  wire  is  said  to  indicate  intensity  currents,  the  other  class 
to  indicate  quantity  currents.  These  two  old  names  survive, 
although  the  fallacious  theory  which  assumed  that  there 
were  two  kinds  of  currents  is  extinct ;  the  term  '  intensity 
galvanometer '  is  used  to  signify  an  instrument  with  thousands 
of  turns  of  thin  wire  in  its  coil,  and  *  quantity  galvanometer ' 
an  instrument  with  few  turns  of  thick  wire.  I  shall  name  the 
two  varieties  *  long  coil '  and  '  short  coil '  galvanometers. 

§  4.  The  student  must  clearly  understand  that  equal  de- 
flections on  the  same  galvanometer  always  indicate  equal 
currents.  These  currents  may  be  flowing  through  very 
different  circuits,  and  any  given  change  may  produce  very 
different  effects  in  the  two  circuits;  but  so  long  as  the 
currents  produce  the  same  deflection  in  the  same  or  equal 
galvanometers,  the  currents  are  equal,  though  the  circuits 
may  be  very  different.  Thus,  using  a  short  coil  galvano- 
meter having  a  resistance  of,  say,  0*1  ohm,  and  no 
other  external  resistance  in  circuit,  a  thousand  voltaic 
cells  in  series  will  produce  about  the  same  deflection  as  one 
cell  of  the  same  kind.  The  thousand  cells  produce  1,000 
times  the  electromotive  force  that  one  cell  does,  but  the 
resistance  of  each  cell,  which  we  may  assume  as  4  ohms,  is 
much  greater  than  that  of  the  short  coil  galvanometer. 
Hence,  the  resistance  of  the  thousand  cells  added  to  that  of 
the  galvanometer  will  be  about  1,000  times  greater  than  that 
of  one  cell  added  to  the  galvanometer,  being  4000-1  in  one 
case,  and  4-1  in  the  other.  The  resistance  varies  in  nearly 
the  same  proportion  as  the  electromotive  force,  and  there- 
fore the  galvanometer  shows  nearly  the  same  deflection, 
indicating  nearly  the  same  current  in  the  two  cases.  In 
the  example  taken  above,  the  thousand  cells  would  give 
a  deflection  greater  than  that  of  the  single  cell  in  the 


CHAP.  XIII.]  Galvanometers.  191 

proportion  of  41  to  40  nearly.  When  a  long  coil  galva- 
nometer, having  a  resistance  of,  say,  8,000  ohms,  is  em- 
ployed, very  different  results  follow.  With  one  cell  perhaps 
no  deflection  is  observable,  whereas  with  one  thousand  cells 
the  needle  is  violently  thrown  against  the  stops  limiting  its 
deflection.  The  cause  is  simple.  With  one  cell  the  resist- 
ance of  the  whole  circuit,  which  will  be  8004,  including  the 
long  thin  wire  of  the  galvanometer,  was  so  great  that  the 
E.  M.  F.  of  one  cell  did  not  give  current  enough  to  deflect  the 
needle ;  but  when  a  thousand  cells  were  employed,  the 
electromotive  force  was  a  thousandfold  greater,  and  the 
whole  resistance  of  the  circuit  was  8000  +  4000,  or  12000 
ohms.  Hence  if  the  E.  M.  F.  of  each  cell  be  taken  as  one 

volt,  the  current  in  the  first  case    will  be   — —  or  nearly 

8004 

0-000125  farads  per  second;  whereas  in   the  second  case 

it  will  be  I00°    or  0*0833,  or  about  666  fold  greater.     The 
12000 

couple  deflecting  the  magnet  of  the  galvanometer  will  also 
be  666  fold  greater  in  the  second  than  in  the  first  case. 
Remark,  however,  that  neither  current  will  be  so  strong  as 
that  produced  when  the  short  coil  galvanometer  was  used ; 

for  in  that  case,  with  a  single  cell  the  current  would  be  — 

4'1 

=  0*244  farad  per  second,  or  roughly  three  times  that  due 
to  the  thousand  cells  as  above  ;  nevertheless  the  couple  ex- 
erted on  the  magnet  of  the  long  coil  galvanometer  would 
be  far  greater  with  0-0833  farad  than  that  exerted  on  the 
short  coil  galvanometer  by  0-244  farad  simply  because  to 
produce  the  same  couple  the  long  coil  galvanometer  would 
only  require  about  three  times  as  many  turns  as  the  short 
coil  galvanometer,  whereas  in  practice  it  would  have  several 
hundred  times  more  turns.  The  greatest  deflection  with 
any  given  circuit  is  obtained  by  using  a  galvanometer,  the 
coils  of  which  have  a  resistance  equal  to  that  of  the  other 
parts  of  that  particular  circuit. 


192  Electricity  and  Magnetism.      [CHAP.  XIII. 

§  5.  The  sensibility  of  any  galvanometer  the  needle  of 
which  is  directed  by  a  magnetic  field  may  be  increased 
by  diminishing  the  intensity  of  the  magnetic  field.  The 
opposing  couple  is  due  to  the  intensity  of  this  field,  and 
by  its  diminution  the  deflection  due  to  a  feeble  current 
may  be  indefinitely  increased.  This  diminution  of  the 
intensity  of  the  original  magnetic  field  is  most  easily 
brought  about  by  laying  a  powerful  magnet  near  the  gal- 
vanometer, in  such  a  position  as  to  counteract  the  earth's 
magnetism,  i.e.  in  the  magnetic  meridian,  with  its  north 
pole  pointing  north.  This  magnet,  often  called  a  com- 
pensating magnet,  is  best  placed  in  the  same  meridian  as 
the  suspended  magnet.  As  the  intensity  of  the  field 
diminishes  under  the  influence  of  this  magnet,  the  rate 
of  oscillation  of  the  suspended  magnet  diminishes,  and  by 
observing  this  rate  we  can  determine  the  increase  of  sensi- 
bility. The  period  of  oscillation  is  inversely  proportional 
to  the  square  root  of  the  intensity  of  the  field,  and  as  the 
directing  couple  is  directly  proportional  to  this  intensity, 
and  the  sensibility  inversely  proportional  to  the  directing 
couple,  we  have  the  sensibility  directly  proportional  to  the 
squares  of  the  periods  of  oscillation.  So  long  as  the 
magnetism  in  the  needle  of  a  galvanometer  remains  un- 
altered, its  relative  sensibility  with  the  compensating  magnet 
at  different  distances  can  be  roughly  computed  in  this 
manner;  I  say  roughly,  because  the  number  of  swings 
which  can  be  counted  is  small  when  the  sensibility  is  great, 
owing  to  the  resistance  of  the  air,  and  this  resistance  would 
also  necessitate  a  correction  in  the  above  series  of  propor- 
tions. This  method  of  obtaining  a  sensitive  galvanometer 
has  the  following  defect :  Inasmuch  as  the  directing  field  is 
due  to  a  difference  between  two  nearly  equal  magnetic  fields, 
a  very  small  change  in  the  direction  or  intensity  of  either  pro- 
duces a  great  change  in  the  difference ;  and  as  the  direc- 
tion and  intensity  of  the  earth's  magnetism  is  perpetually 


CHAP.  XIII.] 


Galvanometers. 


193 


varying,  it  is  nearly  impossible  to  keep  the  needle  pointing  at 
a  constant  fiducial  mark  or  zero,  or  with  a  constant  sensibility. 

The  zero  should  be  adjusted  by  a  much  smaller 
magnet  called  an  adjusting  magnet,  placed  across  the 
lines  of  force  of  the  magnetic  field  or  pointing  east  and 
west,  and  fixed  so  as  to  be  capable  of  adjustment  by 
turning  in  a  plane  perpendicular  to  the  magnetic  meridian, 
and  with  its  centre  in  the  meridian  of  the  suspended  mag- 
net. This  adjusting  magnet  does  not,  when  turned,  alter 
the  intensity  of  the  field  near  the  suspended  magnet,  but 
only  alters  the  direction  of  the  lines  of  force. 

The  suspended  magnet  in  very  sensitive  instruments  should 
be  hung  by  a  single  silk  fibre,  such  as  can  be  obtained  from 
the  silk  threads  in  a  common  silk  ribbon.  The  viscosity  and 
torsional  elasticity  of  this  fibre  put  a  limit  to  the  possible 
diminution  of  directing  force  as  described  above. 

§  6.  The  most  sensitive  instruments  employed  are  those 
known  as  Astatic  galvanometers.  In  these  instruments  two 
magnets  joined  as  in  Fig.  93,  with  the  north  pole  of  one 

FIG.  93.  FIG.  94 


over  the  south  pole  of  the  other,  form  one  suspended  system. 
If  the  two  magnets  had  exactly  equal  moments  with  axes 
precisely  parallel,  they  would  hang  in  equilibrium  in  any 
direction  in  any  uniform  magnetic  field.  The  moment  of  one 


IQ4  Electricity  and  Magnetism.     [CHAP.  XIII 

magnet  always  slightly  exceeds  that  of  the  other,  and  by  this 
excess  directs  the  system.  A  single  galvanometer  coil  may  sur- 
round one  needle,  or,  as  is  obviously  better,  each  needle 
may  have  its  own  coil,  the  two  coils  being  so  joined  that 
the  current  must  circulate  in  opposite  directions  round  the 
two  so  as  to  deflect  both  magnets  similarly.  In  one 
common  form  of  the  astatic  galvanometer,  needles  about 
a  couple  of  inches  long  are  used,  and  their  deflection  is 
observed  by  means  of  a  pointer  or  glass  needle,  A  B,  Fig.  93, 
rigidly  connected  with  the  astatic  system  by  a  prolongation 
of  the  brass  rod  c  D.  This  pointer  oscillates  over  a  gradu- 
ated circle,  and  its  position  is  observed  by  a  microscope  or 
simple  magnifying  glass.  The  coils  are  made  flat,  of  the 
shape  indicated  in  Fig.  93.  To  allow  the  introduction  of 
the,  needle,  the  top  and  bottom  coils  are  made  in  two 
halves,  placed  side  by  side,  with  just  sufficient  space  between 
them  to  allow  the  rod  c  D  to  hang  freely. 

In  Thomson's  mirror  astatic  galvanometer,  Fig.  94,  the 
magnets  are  much  reduced  in  size,  being  only  about  \  in.  long. 
They  are  connected  by  a  strip  of  aluminium  c  D,  and  are  fre- 
quently compound  magnets,  that  is  to  say,  the  top  magnet  is 
replaced  by  four  little  needles,  all  magnetised  to  saturation 
and  placed  with  their  poles  in  one  direction  while  the 
bottom  magnet  is  replaced  by  four  similar  little  needles, 
having  their  poles  also  all  placed  in  one  direction  opposed 
to  that  of  the  upper  system  ;  the  coils  are  made  circular  ; 
the  upper  and  lower  coils  are  each  made  in  two  halves, 
placed  side  by  side.  This  arrangement  gives  the  most 
sensitive  galvanometer  yet  constructed. 

§  7.  A  galvanometer  with  a  single  magnet  directed  by  any 
uniform  magnetic  field,  and  made  with  a  coil  large  in 
diameter  relatively  to  the  length  of  the  magnet  hung  in 
the  axis  of  the  coil,  is  called  a  tangent  galvanometer,  be- 
cause the  tangents  of  the  angles  to  which  the  needle  is 
deflected  by  the  currents  are  proportional  to  the  currents 
causing  the  deflections.  This  law  has  been  proved  above, 
§  3,  Chap.  VIII.  The  best  form  of  tangent  galvanometer  is 


CHAP.  XIII. 


Galvanometers. 


195 


that  in  which  there  are  two  coils  in  parallel  planes,  Fig.  95, 
separated  by  a  distance  equal  to  one-half  their  diameter. 
The  magnet,  which  should  be  short,  is  hung  in  the  common 
axis  of  the  coils  half-way  between  them. 

The  object  of  this  arrangement  is  to  do  away  with  the 
error  due  to  the  sensible  length  of  the  magnet,  and  to 
any  small  deviation  from  a  truly  central  position. 

The  deflection  is  observed  by  means  of  a  light  glass 
pointer  oscillating  over  a  graduated  limb. 

§  8.  A  galvanometer,  whether  astatic  or  not,  with  mag- 
nets directed  by  any  uniform  magnetic  field,  and  having 
the  coils  constructed  so  as  to  be  capable  of  turning  on 
the  axis  round  which  the  magnet  turns,  is  called  a  sine 
galvanometer,  because,  if  the  coils  be  turned  by  hand  so  as 
to  lie  in  a  vertical  plane  parallel  to  that  passing  through 

FIG.  95. 


the  magnet  when  deflected  by  a  current,  then  currents 
deflecting  the  magnet  to  angles  6  and  6{  will  be  to  one 
another  in  the  ratio  of  sin  0  and  sin  0,  :  this  follows  from 
the  considerations  explained  in  §  3,  Chap.  VIII.  Sine  gal- 
vanometers can  be  easily  made  much  more  sensitive  than 
tangent  galvanometers,  because  they  may  be  astatic,  and 
because  the  coils  may  closely  surround  the  magnets.  They 

o  2 


196 


Electricity  and  Magnetism.      [CHAP.  XIII. 


are  inconvenient  for  many  purposes,  because  an  observation 
with  them  occupies  a  longer  time  than  with  any  other 
galvanometer :  each  adjustment  of  the  coils  moves  the 
magnet  also,  and  many  trials  are  necessary  before  per- 
fect parallelism  of  the  planes  is  arrived  at.  This  paral- 
lelism is  attained  by  bringing  a  fiducial  mark  attached  to 
the  coils  vertically  under  a  pointer  attached  to  the  magnet. 
A  vernier  is  attached  to  the  coils,  and  the  angle  through 
which  they  are  turned  from  the  position  indicated  by  the 
fiducial  mark  when  no  current  was  passing  to  that  indicated 
by  the  fiducial  mark  when  the  current  flows  is  read  off  on  a 
graduated  circle.  This  can  be  done  with  great  accuracy. 
The  coils  are  generally  moved  by  a  tangent  screw. 

§  9.  The  form  of  the  coil  in  a  galvanometer  is  not  a 
matter  of  indifference.  The  coil  may  be  too  broad  and  flat, 
or  it  may  be  too  narrow,  to  give  the  greatest  intensity  of 
magnetic  field  which  can  be  produced  by  a  given  length  of 
wire  wound  into  a  coil.  For  a  given  length  and  size  of  wire 
there  is  always  one  form  giving  the  best  effect.  This  form 
has  only  been  determined  for  the  simple  circular  coil  used  in 
the  mirror  galvanometer. 

FIG.  96. 


Xl 


The  form  of  the  curve,  bounding  the  best  section  of  the 


CHAP.  XIII.]  Galvanometers.  197 

coils,  is  given  by  the  following  equation,  due  to  Sir  William 

Thomson  : 

*2  =  («»j,)i  _  j,« 

where  x  is  the  ordinate  measured  in  a  direction  parallel  to 
the  axis  of  the  coil,  y  the  ordinate  perpendicular  to  that  axis 
and  a  the  distance  O  B.  The  origin  of  the  co-ordinates  is  at 
centre  of  the  coil,  where  the  magnet  hangs.  Fig.  96  shows 
the  theoretical  curve  and  a  longitudinal  section  of  a  practi- 
cable coil.  A  portion  of  the  area  enclosed  by  the  curve  near 
the  magnet  is  necessarily  omitted  to  give  room  for  the  magnet 
to  move;  a  practical  approximation  is  made  to  the  best 
form  by  winding  the  wire  on  a  bobbin  of  the  proportions 
shown,  and  filling  with  wire  that  portion  which  is  cross- 
hatched. 

FIG.  97. 


To  get  the  best  result  the  wire  should  not  be  all  of  one 
gauge,  but  should  increase  with  the  diameter  of  the  coil,  so 
that  the  cross  section  of  the  wire  may  be  directly  propor- 
tional to  the  diameter  of  the  coil  at  each  point  :  the  resist- 
ance of  every  turn  of  the  coil  will  then  be  equal.  It  is  prac- 
tically impossible  to  follow  this  plan  rigidly,  but  three  or  four 
sizes  of  wire  may  very  properly  and  easily  be  employed  in 
winding  a  galvanometer  coil. 

§  10.  Sir  William  Thomson  has  given  the  name  of  graded 
galvanometer  to  an  instrument  constructed  as  above,  and 
having  also  amoveable  arm  or  lever  by  which  one  of  the  two 
terminals  /,  Fig.  97,  can  be  connected  by  an  arm  a  c, 


1 98 


Electricity  and  Magnetism.    [CHAP.  XIII. 


hinged  at  c,  with  the  several  stops,  i,  2,  3,  4,  so  as  to 
include  in  the  galvanometer  circuit  either  the  whole  of 
the  wire,  or  f ,  or  £,  or  J,  but  in  all  cases  so  as  to  use  the 
most  efficient  part  of  the  wire  for  the  degree  of  sensibility 
required.  The  relative  sensibility  of  each  grade  is  easily 
determined  by  experiment,  and  is  constant. 

§  11.  Sir  William  Thomson  has  given  the  name  of  dead 
beat  galvanometer  to  a  mirror  galvanometer  having  the 
following  peculiarities  : — i.  very  light  mirror;  2.  four  small 
magnets  at  the  back  instead  of  one  of  equal  weight ;  3. 
the  cell  in  which  the  mirror  moves  only  just  large  enough 
in  diameter  to  allow  the  mirror  to  deflect ;  4.  the  front 

FIG.  98. 
Sectional  Elevation. 


and  back  of  the  cell  so  close  as  each  separately  to  act 
as  a  stop,  preventing  defection  of  the  mirror  beyond  the 
angle  required  to  bring  the  spot  of  light  to  the  end  of  the 
scale.  The  mirror  does  not  strike  the  stops  in  actual  use. 


CHAP.  XIII.] 


Galvanometers. 


199 


With  instruments  so  made  the  spot  of  light  moves  to  the 
final  deflection  without  oscillation  being  checked  by  the 
viscosity  of  the  air.  The  same  end  is  much  less  per- 
fectly attained  in  some  instruments  by  a  vane  of  light 
material  hanging  from  the  magnet.  This  vane  sometimes 
dips  in  water,  and  Mr.  Varley  has  made  galvanometers  in 
which  the  cell  containing  the  magnet  and  mirror  is  full  of 
water. 

§  12.  The  Marine  galvanometer  is  a  galvanometer  adapted 
for  use  at  sea.  It  must  be  so  constructed  that  neither  the 
motion  of  the  ship  nor  the  change  of  direction  produces 

Sectional  Plan. 


sensible  deflections.  This  result  has  been  obtained  by 
Sir  William  Thomson  in  the  following  way  :  The  magnet 
and  mirror  of  a  mirror  galvanometer  are  strung  on  a 
bundle  of  straight  silk  fibres,  stretched  between  A  and  B, 
Fig.  98.  The  suspended  system  is  balanced  so  that  the  axis 


2OO  Electricity  and  Magnetism.      [CHAP.  XIII. 

of  the  fibres  passes  through  its  centre  of  gravity.  A  power- 
ful directing  horse-shoe  magnet,  not  shown  in  the  drawing, 
embraces  the  coils,  and  serves  to  overpower  the  directive 
force  of  the  earth's  magnetism,  the  effect  of  which  on  the 
suspended  magnet  is  moreover  much  weakened  by  a 
massive  soft  iron  case,  enclosing  the  whole  system  every- 
where except  at  the  little  window  D,  by  which  the  rays  of 
light  reflected  by  the  mirror  enter  and  return.  An  adjusting 
magnet  N  s  is  worked  by  a  ratchet  and  pinion  F. 
I  §  13.  The  differential  galvanometer  has  two  equal  coils, 
so  arranged  that  when  the  same  current  or  equal  currents 
pass  through  the  two  coils  in  opposite  directions,  the 
magnet  is  not  deflected.  The  effect  of  one  coil  is  com- 
pletely neutralised  by  that  of  the  other.  The  differential 
galvanometer  is  most  easily  made  by  winding  simultaneously 
two  equal  wires  on  the  coil.  These  two  wires  are  sometimes 
arranged  in  a  sort  of  ribbon  or  plait,  being  joined  by  the 
silk  used  to  insulate  them.  The  accurate  equality  of  the 
magnetic  fields  produced  by  the  two  coils  is  easily  tested, 
for  if  a  current  pass  from  the  battery  first  round  one  coil 
and  then  round  the  other  in  the  opposite  direction,  it 
should,  no  matter  how  great  its  strength,  produce  abso- 
lutely no  deflection.  In  most  cases  a  small  deflection  will 
be  observed,  but  this  is  easily  remedied  by  adding  a  few 
turns  to  the  weaker  coil.  If  after  this  has  been  done  the  resist- 
ance of  one  coil  exceeds  that  of  the  other,  a  length  of  wire 
can  be  added  to  the  coil  of  least  resistance,  and  placed  in 
such  a  position  as  not  to  tend  to  deflect  the  magnet ;  the 
instrument  will  then  be  in  perfect  adjustment.  This  is  a 
very  useful  instrument,  as  we  shall  see  in  a  future  chapter, 
for  the  purpose  of  comparing  resistances.  The  coils  are 
sometimes  made  of  German  silver  instead  of  copper. 
German  silver  has  a  much  greater  resistance  than  copper, 
but  its  resistance  varies  much  less  with  changes  of  tempera- 
ture. In  differential  galvanometers  intended  to  be  used  in 
circuits  otherwise  of  great  resistance,  the  total  resistance  of 


CHAP.  XIII.]  Galvanometers.  2Or 

the  coils  is  of  small  importance,  but  the  equality  of  the 
resistance  of  the  two  coils  is  very  important. 

§  14.  The  sensibility  of  a  galvanometer  may  be  varied 
in  a  very  simple  manner  by  the  use  of  what  is  termed  a 
shunt.  A  shunt  is  a  resistance  coil,  or  coil  of  fine  wire 
used  to  divert  some  definite  portion  of  a  current,  taking 
it  past  a  galvanometer  instead  of  through  its  coils.  Thus  let 
G,  Fig.  99,  represent  the  galvanometer  FIG 

coils,  and  let  s  represent  the  shunt.  Let 
the  resistance  of  the  shunt  be  |th  that  of 
the  galvanometer ;  then,  of  a  total  cur- 
rent passing  from  c  to  D,  9  parts  go 
through  the  shunt  and  do  not  deflect 
the  needle,  while  i  part  goes  through 
the  galvanometer :  only  T^th  of  the 
whole  current  is  therefore  effective  in 
deflecting. the  needle,  and  the  deflec- 
tion (supposing  a  mirror  galvanometer 
be  used)  is  only  y^th  of  what  it  would 
have  been  had  no  shunt  been  used.  Similarly  by  making  the 
shunt  equal  in  resistance  to  ^th  of  the  galvanometric  coil, 
we  reduce  the  sensibility  of  the  instrument  to  the  yi^th  part 
of  its  original  sensibility.  Most  galvanometers  used  for 
measuring  currents  are  now  sold  with  shunts  =  -Jth,  ^th, 
and  -rrl-rrth,  of  the  galvanometer  coil :  by  these  the  sen- 
sibility of  the  instrument  can  be  varied  looofold.  The 
shunts  must  be  made  of  the  same  metal  as  is  used  for  the 
coils,  and  should  be  placed  so  as  to  be  as  nearly  as  possible 
at  the  temperature  of  the  coils.  Calling  s  the  resistance  of 
the  shunt,  and  G  the  resistance  of  galvanometer  coil ; 
calling  d  the  deflection  without  the  shunt,  and  d^  the 
deflection  with  the  shunt,  we  have  quite  generally,  with  a 
given  constant  current  and  assuming  that  the  deflections 
shown  by  the  instrument  are  proportional  to  the  currents  : 
d  :  //,  =  G  +  S  :  s. 

It  must  be  remembered  that  adding  the  shunt  will  in  all 


2O2  Electricity  and  Magnetism.       CHAP.  XIII. 

cases  diminish  the  resistance  of  the  circuit,  so  that  unless 
this  resistance  is  so  great  that  the  resistance  of  the  galvano- 
meter forms  no  sensible  part  of  it,  the  deflections  will  not  be 
altered  in  the  above  proportion.  Let  R  be  the  resistance  of 
all  parts  of  the  circuit  except  the  galvanometer.  Then,  if 
the  E.  M.  F.  remain  constant,  we  have  R  +  G  as  the  total 

resistance  when  no  shunt  is  used,  and  R  -f       G  s    when    the 

G  +S 

shunt  s  is  used.  The  currents  c  and  c}  will  therefore  be  in 
the  proportion  of  R  +  G  S  to  R  +  G  ;  and  compounding 

G   +    S 

this  ratio  with  that  given  above,  we  have  for  d  and  d\  de- 
flections due  to  a  constant  E.M.  F.  with  and  without  the  shunts 
d  :  dx    =  R  (G  +  s)  +  G  s  :  (R  +  G)  s. 

§  15.  Galvanometers  intended  for  circuits  of  extremely  small 
resistance  sometimes  consist  of  a  single  thick  ring  of  copper. 
The  cell  or  battery  used  with  such  a  galvanometer  as  this 
must  be  of  such  construction  as  to  have  very  small  internal 
resistance,  or  no  deflection  will  be  observed.  A  Grove's 
cell  (vide  infra,  Chap.  XIV.  §  14)  with  large  plates  will  give 
a  current  which  can  be  observed  with  a  single  ring  galvano- 
meter. Galvanometers  intended  for  thermo-electric  experi- 
ments must  have  very  small  resistance,  and  are  frequently 
made  with  twenty  or  thirty  turns  of  No.  20  wire  Birmingham 
wire  gauge,  the  diameter  of  which  is  nearly  0-09  centimetres. 
The  resistance  of  these  galvanometers  may  be  less  than 
a  quarter  of  an  ohm.  Galvanometers  intended  for  use  in 
circuits  of  great  resistance  are  frequently  made  with  wire 
of  No.  30  or  No.  36  B.W.G.,  corresponding  to  the  diameters 
0*0305  and  o'oio6  centimetres,  and  the  resistance  of  these 
galvanometers  is  frequently  as  much  as  8,000  ohms.  About 
half  a  yard  of  the  No.  36  gauge  copper  may  have  a  resist- 
ance of  one  ohm,  so  that  the  above  resistance  would  require 
4,000  yards  of  copper  wire.  The  resistance  in  itself  is  a 
defect,  but  it  is  impossible  to  get  a  large  number  of  turns 


CHAP.  XIV.]  Electrometers.  203 

into  a  small  space  without  great  resistance.  It  is  very  im- 
portant that  every  coil  of  the  galvanometer  should  be  per- 
fectly insulated  from  its  neighbour  :  if  any  two  coils  touch  or 
are  connected  through  the  silk,  they  are,  in  technical  lan- 
guage, said  to  be  short-circuited  ;  the  current  does  not  then 
flow  round  any  of  the  intermediate  turns,  and  the  effect  of 
these  is  lost.  When  there  is  no  actual  metallic  contact  there 
may  be  imperfect  and  uncertain  insulation,  and  this  is  the 
worst  defect  a  galvanometer  can  have  :  its  resistance  becomes 
uncertain  and  variable;  the  shunts  can  no  longer  be  de- 
pended upon  as  equal  to  definite  fractions  of  the  resistance, 
and  the  instrument  is  useless  for  accurate  observations. 
The  insulated  wire  should  not  only  be  thoroughly  covered 
with  silk,  but  should  also  be  baked  so  as  to  be  very  dry 
before  being  wound  on  ;  and  after  a  few  layers  have  been 
coiled,  the  bobbin  should  be  baked  again  and  dipped  in 
pure  melted  paraffin.  When  the  coiling  has  been  completed 
the  whole  coil  should  be  again  baked,  and  its  resistance 
compared  with  the  calculated  resistance  of  the  wire  wound  on. 
Contact  between  coils  of  a  differential  galvanometer  is 
obviously  a  radical  defect;  and  when  two  or  more 
distinct  coils  are  wound  on  the  same  bobbin,  as  is  some- 
times done,  these  coils  must  be  very  carefully  insulated. 
Serious  errors  in  testing  have  arisen  from  bad  insulation 
between  different  coils  and  different  parts  of  the  same  coil. 


CHAPTER  XIV. 
// 

t^/r     l/>  ELECTROMETERS. 

§  1.  ELECTROMETERS  indicate  the  presence  ofa  statical  charge 
of  electricity  by  showing  the  force  of  attraction  or  repulsion 
between  two  conducting  bodies  placed  near  together.  This 
force,  depending  in  the  first  place  on  the  quantity  of  electricity 
with  which  the  conducting  bodies  are  charged,  ultimately 
depends  on  the  difference  of  potential  between  them ;  an 


2O4  Electricity  and  Magnetism.      [CHAP.  XIV. 

electrometer  is  therefore  strictly  an  instrument  for  measuring 
difference  of  potential.  It  is  used  often  simply  to  indicate 
the  presence  of  electricity,  but  it  does  not  measure  quantity, 
and  when  used  to  compare  quantities  it  can  do  this  only 
because  under  given  circumstances  the  differences  of 
potential  produced  between  the  two  conductors  are  propor- 
tional to  the  quantities  on  the  bodies  by  which  one  of  the 
conductors  of  the  electrometer  is  successively  charged. 

The  usual  repulsion  electroscopes  have  already  been  de- 
scribed. They  are  known  as  the  pith-ball  or  Canton's  electro- 
scope ;  the  gold  leaf  or  Bennet's  electroscope  and  the  Peltier 
electroscope.  Bohnenberger's  electroscope,  which  consists  of  a 
single  gold  leaf  hanging  between  two  symmetrically  disposed 
knobs  maintained  one  at  a  positive  potential,  and  the  other  at 
an  equal  negative  potential,  belongs  to  a  different  class, 
called  by  Sir  William  Thomson  heterostatic  electroscopes — 
or  instruments  in  which,  besides  the  electrification  to  be 
tested,  another  electrification,  maintained  independently  of 
it,  is  taken  advantage  of.  In  Bohnenberger's  instrument  the 
independent  electrification  maintaining  the  two  knobs  at  a 
constant  difference  of  potential  is  produced  by  a  kind  of 
galvanic  battery  called  a  dry  pile,  consisting  of  thin  plates 
of  two  metals  soldered  together,  and  separated  by  paper 
which  remains  very  slightly  moist  in  consequence  of  contain- 
ing some  deliquescent  material.  Sometimes  the  metal  plates 
are  replaced  by  metals  in  powder  adhering  to  the  paper.  So 
long  as  the  gold  leaf  is  neither  positive  nor  negative,  it  is 
neither  attracted  to  the  right  nor  left ;  positive  electrification 
deflects  it  to  the  negative  knob,  and  vice  versa. 

A  modification  of  Bohnenberger's  electroscope,  Fig.  100, 
may  be  made,  in  which  the  heterostatic  charge  may  with 
advantage  be  given  to  the  gold  leaf,  instead  of  to  the  two 
symmetrically  disposed  bodies  A  and  B.  Any  difference  of 
potentials  between  A  and  B  will  be  indicated  by  the  attrac- 
tion of  the  gold  leaf  to  one  side.  The  higher  the  potential 
of  the  gold  leaf  the  more  sensitive  the  instrument.  The 


CHAP.  XIV.] 


Electrometers. 


205 


high  potential  is  most  easily  maintained  by  connection  with 
a  Leyden  jar. 


FIG.  ioo. 


§  2.  The  most  perfect  form  of  heterostatic  electrometer  yet 
constructed  is  Sir  William  Thomson's  quadrant  electrometer. 
In  this  instrument  the  Bohnenberger's  gold  leaf  is  replaced 


2o6  Electricity  and  Magnetism.       [CHAP.  XIV. 

by  a  very  thin  flat  aluminium  needle,  u,  shown  in  plan,  Fig. 
101,  and  (to  a  smaller  scale)  in  elevation,  Fig.  102.  This  flat 
needle  spreads  out  into  two  wings,  shown  dotted  in  the  plan, 
and  is  hung  by  a  wire  s  from  an  insulated  stem  q  inside  a 
Leyden  jar.  This  Leyden  jar  contains  a  cupful  of  strong 
sulphuric  acid,  the  outer  surface  of  which  forms  the  inner 
coating  of  the  Leyden  jar.  A  wire  z,  stretched  by  a  weight, 
connects  u  with  this  inner  coating. 

A  mirror,  hidden  in  Fig.  102  by  the  metal  cover  /, 
is  rigidly  attached  to  the  needle  u  by  a  rod.  The  mirror 
serves,  as  in  the  reflecting  galvanometer,  to  indicate  the  de- 
flection of  the  needle  u  by  reflecting  the  image  of  a  flarne 
on  to  a  scale.  The  needle  u  hangs  inside  four  quadrants, 
a  b  c  d,  insulated  by  glass  stems,  i  *",  ;  the  quadrant  a  is  in 
electrical  connection  with  */,  and  c  is  in  connection  with  b, 
as  shown  in  plan.  Above  and  below  the  quadrants  two 
tubes,  v  and  01,  at  the  same  potential  as  u,  serve  to  screen  u 
and  the  wires  in  connection  with  it  from  all  induction  ex- 
cept that  produced  by  the  quadrants  abed.  These  quad- 
rants replace  the  bodies  A  and  B  in  the  elementary  form, 
Fig.  100.  Let  us  suppose  u  charged  to  a  high  negative  po- 
tential— then,  if  the  quadrants  are  symmetrically  placed,  it 
will  deflect  neither  to  the  right  nor  to  the  left,  so  long  as  a 
and  c  are  at  the  same  potential.  If  c  be  positive  relatively 
to  a,  the  end  of  u  under  c  and  a  will  be  repelled  from  a  to  c, 
and  at  the  same  time  the  other  end  of  u  will  be  repelled 
from  d  to  b.  The  motion  will  be  indicated  by  the  motion 
of  the  spot  of  light  reflected  by  the  mirror.  Moreover  the 
field  of  force  produced  inside  the  quadrants  is  sensibly 
uniform  just  over  the  narrow  slit  separating  them,  so  that 
the  deflection  will  be  sensibly  proportional  to  the  difference 
of  potential  between  a  and  c.  The  number  of  divisions 
which  the  spot  of  light  traverses  on  the  scale  will  therefore 
in  an  arbitrary  unit  measure  the  difference  of  potential 
between  a  and  c.  This  instrument  is  therefore  an  electro- 
meter, and  not  a  mere  electroscope.  Two  terminals/,  of 


CHAP.  XIV.]  Electrometers.  207 

which  only  one  is  shown  in  the  drawing,  serve  to  charge  a 
and  c :  they  can  be  lifted  up  out  of  contact  with  a  and  c  after 
charging  them.  A  third  terminal,  /,  serves  to  charge  the 
Leyden  jar.  It  is  usually  disconnected  from  the  inner  coat- 
ing by  being  turned  back,  so  that  the  tongue  M  is  discon- 
nected from  the  metal  rod  behind  s. 

With  good  glass,  carefully  washed  in  distilled  water  and 
dried  before  the  fire,  before  being  filled  with  sulphuric  acid, 
the  Leyden  jar  can  be  made  to  insulate  so  well  as  not  to  lose  a 
quarter  per  cent,  of  its  charge  per  diem.  Sir  William  Thom- 
son adds  a  little  inductive  electrical  machine  inside  the  jar 
(§  i,  Chapter  XIX.),  by  which  the  charge  can  be  increased 
or  diminished  at  will,  and  also  a  gauge  by  which  the 
constancy  of  the  charge  can  be  measured.  An  instrument 
of  this  class  may  be  made  so  sensitive  as  to  give  a  deflection 
of  100  divisions  for  the  difference  of  potential  between  zinc 
and  copper. 

§  3.  The  essential  parts  of  Sir  William  Thomson's/^r/^/<? 
electrometer  are  shown  in  Fig.  103.  g  is  a  flat  insulated 
disc  to  which  the  charge  to  be  measured  may  be  communi- 
cated, h  is  a  second  insulated  disc,  having  an  opening  at 
the  centre  filled  by  a  very  light  aluminium  plate/,  supported 
by  a  stretched  wire  *  /,  and  carrying  an  index  arm  below 
the  plate  h.  This  plate  and  wire  are  shown  in  Fig.  57, 
p.  100.  If  now  g  and  h  are  at  the  same  potential,  there 
will  be  no  charge  on  the  opposed  faces,  and/"  will  neither  be 
attracted  nor  repelled  by^.  If  a  charge  of  electricity  be  com- 
municated to  g  or  h,  so  that  the  potentials  differ,  /  will  be 
attracted  or  repelled  by  g,  and  the  consequent  motion  can  be 
read  by  observing  at  /  the  position  of  a  little  hair,  fixed  to  the 
index  arm.  Unless,  however,  the  charges  on  g  and  h  are 
very  great,  the  forces  will  be  very  small,  and  this  arrange- 
ment would  offer  little  advantage  :  its  sensibility  is  enor- 
mously increased  by  the  following  device  :— A  considerable 
permanent  charge  is  given  to  h,  which  is  maintained  in 
permanent  connection  with  a  highly  charged  perfectly 


208  Electricity  and  Magnetism.       [CHAP.  XIV. 

insulated  Leyden  jar ;  then  if  g  be  in  connection  with  the 
earth,  a  charge  will  be  induced  on  g,  and  /  will  be  attracted 
by  that  charge  with  a  very  sensible  force.  Let  the  torsion  of 
the  wire  *  *  be  adjusted  so  as  to  depress  /or  elevate  the  hair 
near  /,  then  there  will  for  a  given  potential  of  h  be  one  distance 


FIG.  103. 


Fi<;.  103  a. 


between  g  and  h,  at  which  the  electrical  attraction  will  just 
balance  the  torsion  of  the  wire.  The  distance  of  the  plate 
g  from  the  plate  h  can  in  the  instrument  be  adjusted  by  a 
fine  screw,  and  this  position  is  read  off  by  a  divided  scale  and 
vernier.  Let  g  next  be  disconnected  from  the  earth  and  con- 
nected with  the  body  the  potential  A  of  which  is  to  be  tested, 
i.e.  compared  with  that  of  the  earth — a  new  charge  will  be 
induced  on  ^-proportional  to  the  difference  between  the  poten- 
tial of  h  and  A  ;  if  A  be  positive,  assuming  the  potential  of  h  to 
be  positive  also,  the  charge  will  be  less  than  that  due  to  the 
earth,  and  plate  g  must  be  lowered.  If,  on  the  contrary,  A  be 
negative,  the  charge  will  be  greater  than  that  due  to  the  earth, 
and  to  bring  the  hair  at  /  back  to  its  fiducial  mark  g  will  have 


CHAP.  XIV.]  Electrometers.  209 

to  be  raised — the  difference  of  potential  between  A  and  the 
earth  will  be  proportional  to  the  distance  through  which  g 

is  moved  ;  for,  from  §  7,  Chapter  V.,  we  have/  =    -^ — —2  • 

O     7T    d 

where  v  is  the  difference  of  potential  between  two  plates  at 
a  distance  a.  When  /is  at  the  fiducial  mark, /determined 
by  the  torsion  of  the  wire  is  eonstant,  and  the  quotient 

—  =  -  must  also  be  constant,  so  that  the  difference  of  po- 
a2  a 

tential  v  must  vary  in  direct  proportion  to  the  distance  a 
between  the  plates,  in  order  to  balance  this  constant  force. 

Each  looth  of  an  inch  corresponds  therefore  with  a  given 
potential  of  the  plate  h  to  a  perfectly  definite  and  constant 
difference  of  potential,  so  that  if  with  one  body  A  the  disc  g 
requires  to  be  raised  0*01  above  the  position  when  the 
earth  reading  was  taken,  and  with  a  second  body  B  the  same 
plate  requires  to  be  raised  o'i  above  the  same  position,  we 
know  that  the  potential  of  B  is  ten  times  that  of  A,  both 
potentials  being  above  or  below  that  of  the  earth.  By 
making  the  potential  of  h  in  all  cases  large,  the  distance  a 
may  also  be  large  for  a  constant  force  /  and  a  great  range 
of  measurement  is  thus  combined  with  great  sensibility. 

The  plate  h  h  forms  part  of  the  inner  armature  of  a 
Leyden  jar,  the  glass  of  which  is  lettered  m  m  ;  the  micro- 
meter screw  b  serves  to  raise  and  lower  the  insulated  plate  g 
by  means  of  a  slide  which  need  not  be  specially  described 
here.  The  position  ofg  is  read  off  by  a  vertical  scale  not  shown, 
still  further  subdivided  by  the  divided  ring  at  q ;  the  plate^  is 
connected  with  a  terminal  s,  shown  in  Fig.  1030,  projecting 
outside  the  Leyden  jar  through  an  opening  in  the  case.  This 
rod  t  serves  to  charge  the  plate  gt  and  is  usually  covered 
with  a  cap,  t,  of  special  form,  intended  to  prevent  the  influx 
or  efflux  of  air.  When  the  instrument  is  not  in  use,  the 
cap  /  is  pushed  down,  closing  the  Leyden  jar  entirely. 
When  the  instrument  is  in  use,  the  cap  /  is  raised,  and 
being  then  wholly  insulated  it  serves  as  the  terminal  by 

p 


210  Electricity  and  Magnetism.      [CHAP.  XIV. 

which  to  charge  g.  A  lead  case  for  pumice  stone  and 
sulphuric  acid  is  placed  inside  the  Leyden  jar  to  dry  the 
air.  The  Leyden  jar  can  be  charged  by  an  insulated 
rod,  introduced  temporarily  through  a  little  opening. pro- 
vided for  the  purpose  in  the  top  of  the  case.  When  the  jar 
is  once  charged  this  hole  is  closed  by  a  screw.  When  pro- 
per glass  is  chosen  for  the  jar,  well  washed  with  distilled 
water,  and  dried  by  evaporation  before  the  fire  before  being 
finally  closed,  the  Leyden  jar  will  not  lose  J  per  cent,  of  its 
contents  per  diem.  Care  must  be  taken  to  remove  the  pu- 
mice stone  once  a  month  and  bake  it,  otherwise  the  sul- 
phuric acid  diluted  with  water  attracted  from  the  atmosphere 
will  overflow  and  spoil  the  instrument.  The  difference  of 
potential  produced  by  the  contact  of  zinc  and  copper  may 
be  detected  on  this  instrument,  and  the  electromotive  force 
of  20  or  30  Daniell's  cells  can  be  measured  with  considerable 
accuracy.  The  value  of  each  division  of  the  instrument 
alters  as  the  charge  in  the  Leyden  jar  varies.  The  instru- 
ment is  not  an  absolute  electrometer,  but  is  used  to  compare 
potentials  as  galvanometers  are  used  to  compare  currents. 
It  is  specially  adapted  for  experiments  on  the  potential  of 
the  atmosphere.  If  a  burning  match  be  attached  to  the 
terminal  s,  the  plate  g  is  rapidly  brought  to  the  potential  of 
the  air  at  the  point  where  the  match  burns.  The  instrument 
is  held  in  one  hand,  the  position  of  the  hair  at  /  relatively  to 
the  fiducial  mark  observed  through  the  magnifying  glass,  and 
the  plate  g  adjusted  by  moving  the  screw  head  w.  In  the 
manufacture  of  the  instrument  so  much  torsion  should  be 
given  to  the  wire  as  will  just  leave  the  plate  f  in  stable 
equilibrium  when  /  is  at  the  fiducial  mark.  When  very  little 
initial  torsion  is  given,  the  directing  force  of  the  wire  varies 
very  rapidly  with  the  increased  angle  through  which  it  is 
turned  by  the  attraction  or  repulsion  of  plate  f,  and  the 
equilibrium  is  then  very  stable.  As  more  initial  torsion  is 
given,  the  change  of  directing  force  due  to  a  deflection  from 
the  fiducial  point  is  less,  and  the  equilibrium  may  easily  be 


CHAP.  XV.]  Galvanic  Batteries.  21 1 

made  quite  unstable.  The  torsion  used  should  be  a  little 
less  than  that  giving  instability  for  the  lowest  position  in 
which  g  will  be  used. 

§  4.  The  absolute  electrometer  is  an  instrument  much 
like  the  portable,  but  on  a  larger  scale,  and  so  arranged  that 
the  actual  force  on  the  moveable  disc  can  be  measured. 
Then,  calling  v  and  Vj  the  two  differences  of  potentials  which 
give  the  same  force  F  with  the  two  distances  D  and  D!  be- 
tween the  parallel  plates,  and  calling  A  the  area  of  the  move- 
able  plate,  we  have 


by  which  equation  the  difference  of  potential  v  —  v,  is 
given  in  absolute  electrostatic  units  :  from  measurements  of 
this  kind  we  can  determine  the  constant  multipliers  required 
to  convert  the  indications  of  a  quadrant  or  portable  elec- 
trometer into  absolute  measure. 


CHAPTER  XV. 

GALVANIC   BATTERIES. 


C*) 


§  1.  THE  simplest  form  of  galvanic  cell  practically  in  use 
consists  of  a  plate  of  zinc  and  a  plate  of  copper,  immersed 
in  water  slightly  acidulated  by  the  addition  of  a  little 
sulphuric  acid.  The  zincs  and  coppers  are  generally 
soldered  together  in  pairs,  and  placed  in  a  long  stoneware 
or  glass  trough,  divided  into  separate  cells  by  partitions  as 
shown  in  Fig.  104.  This  battery  is  made  more  portable  by 
filling  the  cells  with  sand,  which  supports  the  plates  and 
prevents  the  liquid  from  splashing  about  when  the  trough  is 
moved.  In  this  form  it  is  called  the  common  sand  battery. 
The  copper  is  advantageously  replaced  by  platinum  or 
platinized  silver ;  this  battery  without  sand  is  then  known 
*  r  2 


212 


Electricity  and  Magnetism.        [CHAP.  xv. 


as  Sme^s  battery.  The  rough  surface  of  the  deposited 
platinum  seems  to  have  the  effect  of  diminishing  polarisa- 
tion. Fig.  105  shows  a  common  form  of  one  cell  of 

FIG.  104. 


Smee's  battery  ;  the  plate  of  platinized  silver  hangs  from  a 
wooden  bar  between  two  plates  of  zinc  amalgamated  with 

FIG.  105.  FIG.  IOSA. 


mercury ;  the  brass  terminals  serve  to  hold  the  three  plates 
together. 

In  Walker's  battery  the  copper  is  replaced  by  graphite. 

§  2.  The  following  are  the  chief  merits  of  a  galvanic  cell  : 

1.  It  should  produce  a  high  electromotive  force. 

2.  It  should  have  small  and  constant  internal  resistance. 

3.  Its  electromotive  force  should  be  constant  whether  it 
be  employed  in  producing  a  large  or  small  current. 

4.  The  materials  it  consumes  should  be  cheap. 

5.  No  materials  should  be  consumed  except  when  the 
battery  is  employed  to  produce  a  current. 


CHAP.  XV.]  Galvanic  Batteries.  213 

6.  The  form  should  be  such  that  the  condition  of  the 
cells  can  easily  be  seen,  and  fresh  materials  added  when 
required. 

No  one  battery  combines  all  these  advantages  in  the 
highest  degree,  and  the  special  requirements  of  each  case 
should  guide  us  in  the  choice  of  the  design  to  be  preferred  for 
any  given  purpose. 

§  3.  No  single-fluid  cell  can  give  a  constant  electro- 
motive force  because  of  the  polarization  of  the  plates,  §  9, 
Chapter  IV.  The  electromotive  force  due  to  the  metals 
in  the  batteries  above  described  diminishes  with  extra- 
ordinary rapidity  as  soon  as  the  poles  are  joined,  especially 
when  the  current  flowing  is  considerable.  This  diminution 
is  due  to  an  opposed  E.  M.  F.  consequent  chiefly  on  the 
presence  of  free  hydrogen  on  the  copper  or  platinum 
plate.  The  effect  of  gases  in  setting  up  an  electromotive 
force  is  easily  shown  by  the  voltameter,  Fig.  41,  p.  67.  Let  the 
wires  A  and  B  be  joined  by  a  wire,  part  of  which  is  the 
coil  of  a  galvanometer.  A  current  will  be  perceived 
opposed  in  direction  to  that  which  decomposed  the  water ; 
it  will  come  from  the  hydrogen,  through  the  water  to  the 
oxygen.  This  current  is  accompanied  by  the  recombina- 
tion of  oxygen  and  hydrogen  forming  water.  The  direction 
of  the  current  from  this  gas  cell  is  such  as  would  be  pro- 
duced if  hydrogen  were  a  negative  metal  electrode,  and 
oxygen  a  positive  electrode,  as  shown  in  Fig.  1050. 
Provided  the  oxygen  and  hydrogen  have  no  chemical 
affinity  for  the  'metal  employed  to  join  them,  this  metal  will 
have  no  effect  on  the  E.  M.  F.  of  the  gas  cell ;  the  hydrogen 
plays  the  part  of  the  zinc  plate,  being  oxidised  by  the 
water,  and  the  hydrogen  set  free  appears  at  the  positive 
electrode  (oxygen)  and  combines  with  it.  The  fact  that 
hydrogen  and  oxygen  joined  by  a  metal  conductor  will 
recombine,  whereas  when  simply  in  presence  of  one 
another  they  will  not  recombine,  is  probably  due  to  the 
electromotive  force  set  up  at  the  junction  between  the 
metals  and  the  gases  Thus  the  junction  between  the 


214  Electricity  and  Magnetism.        [CHAP.  XV. 

platinum  and  hydrogen  makes  the  hydrogen  positive ;  the 
oxygen  is  either  less  positive  or  negative  :  thus  the  difference 
of  potentials  produced  by  the  contacts  tends  to  produce  a 
current  from  the  hydrogen  electrode  to  the  oxygen  elec- 
trode through  the  water,  and  this  would  decompose  the 
water,  sending  hydrogen  to  the  oxygen  electrode,  and 
oxygen  to  the  hydrogen  electrode.  The  result  is,  that  the 
decomposition  of  the  water  is  balanced  by  the  recomposi- 
tion  at  the  electrodes,  and  the  gas  gradually  absorbed. 
The  whole  of  the  gas  cannot  be  thus  absorbed  consistently 
with  the  theory  of  dissipation  of  energy.  The  above 
illustration  of  the  action  of  the  gases  certainly  is  not  a 
complete  or  accurate  hypothesis.  If  it  were,  the  electro- 
motive force  of  the  gas  cell  or  polarized  platinum  plates 
would  be  constant,  whereas  it  is  much  increased  if  the 
decomposition  of  the  water  has  been  effected  by  a  high 
E.  'M.  F.,  and  gradually  diminishes  as  the  recombination  of 
the  gases  occurs,  as  we  should  expect  from  the  theory  of 
dissipation  of  energy. 

The  electromotive  force  called  up  by  the  deposition  of 
gases  on  electrodes  is  within  limits  nearly  proportional  to 
the  E.  M.  F.  employed  in  producing  the  deposition.  This 
is  most  clearly  seen  when  the  electrodes  are  so  formed  that 
the  gases  cannot  easily  escape — when,  for  instance,  the 
electrodes  are  small  surfaces  of  metal,  surrounded  by  an 
insulator,  such  as  are  produced  by  boring  a  hole  so  as  to  lay 
bare  a  small  portion  of  the  copper  of  a  guttapercha- covered 
wire.  We  may,  perhaps,  conceive  the  high  E.  M.  F.  produced 
in  reaction  against  a  great  decomposing  E.  M.  F.  as  due  to  the 
decompositions  of  a  row  of  molecules  forming  a  number  of 
gas  cells  in  series  imperfectly  insulated  from  one  another. 

§  4.  The  sand  battery  is  the  worst  of  all  batteries  as  regards 
constancy  of  electromotive  force,  the  polarization  being 
greater  in  this  battery  than  in  any  other  because  the  gas 
cannot  readily  escape.  The  common  copper  and  zinc  cell 
is  the  next  in  order  of  demerit.  Its  electromotive  force  can 
at  any  time  while  it  is  producing  a  current  be  greatly  in- 


CHAP.  XV.]  Galvanic  Batteries.  215 

creased  by  mechanically  brushing  the  gases  off  the  metals, 
or  even  by  shaking  the  battery.  The  Smee  battery  is  better 
than  the  copper  zinc  battery  because  it  is  found  that  hydrogen 
does  not  stick  to  the  finely  divided  platinum  on  the  surface 
of  the  plates  so  much  as  to  the  copper.  The  carbon  or 
graphite  plate  in  Walker's  battery  performs  the  same  func- 
tion of  facilitating  the  liberation  of  the  free  hydrogen. 

When  any  of  these  single  fluid  batteries  are  left  with  the 
electrodes  free  or  insulated  so  that  no  current  passes,  the 
full  electromotive  force  is  gradually  restored,  partly  by  the 
liberation  of  the  hydrogen,  partly  by  its  recombination 
with  oxygen.  The  process  of  restoration  may  be  assisted 
by  passing  a  current  through  the  cells  against  their  E.  M.  F. 

For  some  purposes  a  constant  current  is  not  required  ; 
— for  instance,  where  batteries  are  employed  to  ring  bells  in 
houses  or  on  railway  lines  they  have  long  intervals  of 
repose ;  for  such  purposes  single  fluid  batteries  are  still 
employed  en  account  of  their  simplicity. 

§  5.  The  manner  in  which  the  electrolyte  employed  in  a 
cell  modifies  the  electromotive  force  in  an  unclosed  circuit, 
according  to  the  contact  theory,  has  already  been  explained. 
(Chap.  II.  §  22.)  When  the  circuit  is  closed  the  same 
electromotive  force  exists  so  long  as  the  surfaces  in  contact 
remain  unmodified  ;  it  is  easy  to  see  by  the  contact  theory 
that  considerable  changes  may  be  introduced  by  what  is 
called  polarization,  i.e.  by  the  deposition  on  the  metallic 
surfaces  of  electrolysed  substances.  When  no  such  change 
occurs,  the  change  of  potential  at  each  surface  of  separation 
is  the  same  in  the  closed  as  in  the  unclosed  circuit.  Calling 
E!,  E2,  E3,  &c.  the  successive  values  of  the  E.  M.  F.  at  each 

surface,  the  whole  current  c= — — ,  where  the  symbol  2 

•^  .  R 

denotes  that  all  the  successive  values  of  E  or  R  have  been 
added.  If  now  any  part  o  of  the  circuit  be  brought  to  the 
potential  zero,  the  potential  of  v  at  any  point  a  is  equal  to 

va      TJ 

— H™E,  where  2£  means  that   the   summation  of  the 


216  Electricity  and  Magnetism.       [CHAP.  XV. 

several  values  of  R  and  of  E  is  made  between  the  points  o 
and  a.  The  value  of  E  is  positive  in  each  case  when  the 
change  at  the  surface  of  separation  in  question  increases  the 
difference  of  potential  between  a  and  o. 

But  in  §  8,  Chap.  XI.  another  theory  was  explained  by 
which  the  electromotive  force  of  a  battery  could  be  calcu- 
lated simply  from  the  chemical  action  in  the  cell.  In  order 
that  these  theories  may  be  consistent,  a  certain  relation 
must  exist  between  the  electromotive  forces  due  to  contact 
in  the  circuit  and  the  thermal  equivalent  of  the  chemical 
actions  in  the  cell.  This  relation  may  be  stated  as  follows : 
Consider  a  single  fluid  cell  of  three  materials  c,  A,  z,  of 
which  A  is  the  electrolyte;  let  ECA,  EAZ,  EZO  be  the  three  electro- 
motive forces  at  the  three  surfaces  of  separation ;  then  by  the 
paragraphs  already  cited  we  have  EOA+EAZ  +  EZO=J  .  S .  0e , 
when  2  .  de  signifies  the  sum  of  the  quantities  of  heat  which 
would  be  generated  and  consumed  by  reactions  equal  to 
those  which  take  place  in  the  cell  per  unit  of  time  when  the 
unit  current  is  passing. 

The  following  consequences  are  deduced  from  this  law: — 

1.  The  difference   of  potentials  between  any  two  metals 
c  and  z  not  in  contact  plunged  in  a  cell  with  one  or  more 
fluids  is  equal  to  the  difference  j(S .  0e)— EZO;  hence  the 
electromotive  force  of  any  combination,  although  it  may  be 
calculated  by  the  contact  theory,  really  depends  wholly  on 
the  chemical  action ;  for  the  effect  of  the  electrolyte  is  simply 
to  increase  or  decrease  the  E.  M.  F.  due  to  the  contact  be- 
tween the  metals  by  just  so  much  as  is  required  to  give  the 
E.  M.  F.  determined  by  the  chemical  theory. 

2.  With  a  given  electrolyte  the  metals  may  be  ranged  in 
contact  series,  so  that  the  electromotive  force  between  any 
pair  (in  an  incomplete  cell)  will  be  equal  to  the  difference 
between  the  numbers  affixed  to  each  metal  in  the  series. 
The  numbers  for  this  series  might  either  be  directly  observed 
or  they  might  be  deduced  for  groups  of  three  metals  from 
observed  electromotive  forces  due  to  three  combinations  of 
these  three  metals  in  pairs  with  the  electrolyte.     This  con- 


CHAP.  XV.]  Galvanic  Batteries.  2\J 

sequence  follows  from  the  contact  theory  unaided  by  the 
electro-chemical  theory. 

3.  Let  the  electromotive  force  of  a  complete  cell  C|A]Z|C 
be  known,  also  that  of  F|A|Z|F,  where  the  terminal  metal  is 
changed;  then  the  electromotive  force  of  the  complete  cell 
C|A|F|C,   composed   of  the   same    electrolyte  and   the   two 
terminal  metals,  is  equal  to  the  difference  between  the  two 
others.     It  need  hardly  be  remarked  that  C|A|F|C=—  F|A|C|F. 

4.  The  difference  of  potentials  between  any  two  metals 
c  and  z  plunged  in  a  single  electrolyte  A  must  be  equal  to 
j(0z£z— 0C£C)  —  Ezc?  where  flz  and  fz  are  the  values  proper  to  the 
reaction  which  takes  place  between  z  and  A  when  z  is  the 
negative  metal  of  a  cell,  and  0ce0  the  values  when  c  is  the 
negative  metal  of  a  cell,  with  the  same  electrolyte.     For  let 
the  two  metals  be  used  in  two  cells  with  a  third  metal  p 
such  that  in  both  cases  p  is  the  positive  metal  which  is  not 
attacked.     Then  the  change  in*  the  electromotive  force  of 
the  complete  cell  is  simply  the  change  in  the  chemical  action 
or  j(0zez— 0C£C),  and  hence  the  change  in  the  incomplete  cell 
must  be  that  stated  above ;  but  this  change  in  the  E.  M.  F. 
due  to  the  substitution  of  one  metal  for  another  must  by 
the   second   corollary  be    the  electromotive   force   of  one 
metal  relatively  to  the   other  when  they  are  both  in  one 
solution.     It  follows  that  if  no  chemical  action  takes  place 

^  j(0z£z— 0cfc)  —  Ecz=o;  or  the  electrolyte  if  it  attacks  neither 
metal  must  act  as  a  solid  conductor. 

5.  With  different  electrolytes  the   contact  series  of  the 
metals  will  differ,  inasmuch  as  the  differences  between  6e  for 
the  same  pair  of  metals  will  be  different  for  different  re- 
actions. 

6.  The  degree  of  concentration  of  a  solution  used  in  a 
cell  can  only  affect  the  E.  M.  F.  so  far  as  it  changes  the  value 
of  Qe  for  the  same  reaction.    Since  a  change  of  concentration 
does  affect  to  some  extent  the  value  of  the  E.  M.  F.  it  appears 
to  follow  that  the  work  required  to  produce  a  given  reaction 
varies  with  the  degree  of  concentration. 

7.  No  change  in  the  electromotive  force  of  a  cell  can 


218  Electricity  and  Magnetism.       [CHAP.  XV. 

result  from  the  substitution  of  one  thoroughly  inert  substance, 
if  there  be  such,  for  another  as  the  positive  pole.  Calling  E^ 
the  electromotive  force  of  the  surface  of  the  inert  substance, 
and  the  active  metal  and  EAX  the  electromotive  force  between 
the  electrolyte  and  the  inert  substance,  E^+E^  must  for  x 
be  constant  with  all  metals.  If  with  apparently  inert  sub- 
stances some  change  does  result,  it  proves  that  the  substance 
is  not  inert. 

8.  The  presence  of  any  inert  substance  in  the  electrolyte 
cannot  change  the  E.  M.  F.  of  the  combination,  but  might 
possibly  change  the  distribution  of  potential. 

9.  Polarization  must  be  accompanied  by   a   change   in 
chemical  action.  On  the  contact  theory  it  is  easy  to  see  how 
polarization  changes  the  E.  M.  F.     Thus  it  is  common  to  say 
that  in  the  simple  copper  zinc  cells  the  copper  is  plated  with 
hydrogen.     The  presence  of  hydrogen  changes  the  series  of 
surfaces  in  contact,  and  by  corollary  4  the  difference  between 
a  cell  with  hydrogen  and  a  cell  with  copper  for  instance  will 
be  equal  to  j(0Y— 0'V')-EHO,  where  0Y  and  8"e"  are  the 
quantities  of  heat  corresponding  to  the  combination  of  an 
electro-chemical   equivalent   of  hydrogen    and    of  copper 
respectively  with  certain  elements  of  the  electrolyte,  and  EHO 
is  the  electromotive  force  due  to  copper  and  hydrogen;  but 
in  order  that  this  difference  may  not  be  zero  the  sum  of  J0e 
throughout  the  cell  must  be   changed;    since   polarization 
does  alter  the  E.  M.  F.  of  a  cell,  this  proves  that  the  dis- 
engagement of  free  hydrogen  against  a  surface  of  nascent 
hydrogen  attached  to  a  metal  requires  a  different  amount 
of  work  from  that  required  to  deposit  nascent  hydrogen 
on  the  metal.     While  polarization  is  proceeding  one  of  the 
series  of  chemical  actions  in  the  cell  is  the  formation  of 
an  amalgam  of  hydrogen  with  the  metal  plate;  when  this 
no  longer  continues,  the  E.  M.  F.  becomes  constant.     The 
action  between  the  hydrogen  and  the  clean  metal  assists  the 
current,  and  its  intensity  dies  out   as   the  metal  becomes 
saturated.    When  the  current  ceases  the  affinity  of  what  may 
be  termed  the  amalgamated  hydrogen  for  the  oxygen  of  the 


CHAP.  XV.]  Galvanic  Batteries.  219 

water  overcomes  the  affinity  of  the  hydrogen  for  the  metal, 
and  a  reverse  current  ensues.  This  current  becomes  weaker 
and  weaker  as  the  hydrogen  leaves  the  metal,  for  its  affinity 
(if  the  word  may  be  used)  increases  as  the  metal  becomes 
less  and  less  saturated.  The  equivalence  between  the 
current  produced  by  polarization  and  the  work  done  in 
producing  polarization  by  a  current  is  obvious  on  this 
hypothesis. 

10.  Very  considerable  changes  in  the  E.  M.  F.  of  contact 
between  two  metals  result  from  a  change  in  their  molecular 
condition  or  tempering  or  state  of  crystallisation,  but  these 
differences  will  make  very  little  change  in  the  E.  M.  F.  of  the 
circuit,  being  almost  wholly  compensated  by  the  change  in 
the  differences  of  potential  at  the  surfaces  separating  the 
electrolyte  from  the  metals.  They  would  be  exactly  com- 
pensated if  the  work  required  to  produce  the  given  chemical 
reactions  in  the  cell  were  constant,  but  where  the  molecular 
condition  of  the  metals  varies,  this  work  will  not  be  quite 
constant. 

,  §  6.  The  true  absolute  values  of  the  electromotive  force 
produced  by  unpolarized  single  fluid  elements  are  not 
accurately  known,  and  owing  to  the  polarization  produced 
by  any  current  cannot  be  determined  by  galvanometric 
observations.  This  is  of  less  consequence,  because,  not 
being  constant,  the  value  of  this  electromotive  force  could 
not  be  used  in  any  formulae  depending  on  Ohm's  law.  The 
available  electromotive  force  in  a  Smee's  element  is  about 
0*47  of  a  volt 

The  solution  employed  has  little  effect  on  the  electro- 
motive force,  but  has  a  great  effect  on  the  resistance. 
Pure  water  has  a  much  higher  resistance  than  any  of 
the  solutions  employed  in  batteries  :  hence  a  cell  with  pure 
water  or  nearly  pure  water  will  give  only  a  very  feeble 
current  through  an  external  circuit  of  small  resistance ; 
when  salt,  or  sulphuric  or  nitric  acid  are  added,  the  current 
is  increased  at  once.  This  is  due  merely  to  the  change  in 
the  total  resistance  of  the  circuit,  not  to  any  increase  of 


220 


Electricity  and  Magnetism.         [CHAP.  XV. 


electromotive  force.  A  solution  of  sulphuric  acid  and 
water  containing  thirty  per  cent,  of  sulphuric  acid  has  a 
smaller  resistance  than  a  solution  with  either  less  or  more 
sulphuric  acid ;  but,  when  used  to  charge  a  battery,  it  gives 
rise  to  useless  oxidation  of  the  zinc — useless  because  it 
produces  no  current  outside  the  cell.  Much  weaker 
solutions,  of  about  one  part  in  twelve,  are  therefore  com- 
monly employed ;  solutions  of  common  salt  and  of  sulphate 
of  zinc  are  also  employed  to  charge  the  battery ;  the  first 
because  of  its  small  resistance  and  the  second  because  the 
action  of  the  cells  causes  no  change  in  the  constituents  of 
the  solution. 

§  7.  Some  useless  oxidation  of  the  zinc  or  other  electrode 
which  is  consumed  in  the  cell  almost  always  occurs,  and 
is  due  to  what  is  called  local  action.  This  local  action 
arises  from  inequalities  in  the  condition  of  the  zinc  exposed 
to  the  liquid.  These  inequalities  cause  certain  points  of  the 
zinc  to  be  electro-negative  to  certain  other  points.  These 
points  being  in  metallic  connexion  through  the  mass  of  the 
zinc  constitute  with  the  fluid  a  galvanic  cell  of  small  E.  M.  F., 
but  also  of  very  small  resistance,  and  a  current  is  produced  in 
a  local  circuit  as  indicated  by  arrows  in  Fig.  106  :  that  portion 
of  the  zinc  which  is  most  electro-positive  is  eaten  away, 
and  the  current  produced  is  con- 
fined to  the  cell,  and  cannot  be 
utilized.  This  local  action  is 
very  much  increased  by  dimi- 
nishing the  resistance  of  the 
fluid.  It  is  much  diminished  by 
amalgamating  the  surface  of  the 
zinc.  This  is  done  by  cleaning 
the  surface  of  the  zinc  plates 
with  dilute  sulphuric  or  hydro- 
chloric acid,  and  then  rubbing  a 
little  mercury  over  the  surface 

with  a  brush.  The  surface  being  then  composed  of  a  uni- 
form material  not  susceptible  of  those  differences  of  temper 


FIG.  106. 


CHAP.  XV.] 


Galvanic  Batteries. 


221 


described  by  the  words  '  hard '  and  '  annealed '  is  not  attacked 
by  the  solution  until  the  external  circuit  is  closed  :  no  zinc 
is  consumed  except  in  producing  useful  currents.  Several 
forms  of  battery  are  in  use  in  which  the  zinc  plate  is  kept 
permanently  in  contact  with  a  small  supply  of  mercury. 

§  8.  Single  fluid  batteries  are  subject  to  another  incon- 
venience besides  that  of  polarization ;  the  solution  usually 
employed  cannot  by  any  convenient  means  be  kept  in 
uniform  condition.  For  instance,  the  sulphuric  acid  used 
in  most  forms  of  the  cell  is  gradually  us^d  as  well  as  the 
zinc,  so  that  the  resistance  of  the  battery  is  perpetually 
increasing,  and  the  cell  requires  from  time  to  time  to  be 
refreshed,  as  it  is  termed,  by  the  addition  of  sulphuric  acid. 
Single  fluid  batteries  are  subject,  therefore,  to  three  defects  : 
their  electromotive  force  is  enfeebled  by  polarization ;  it  is 
not  constant ;  and  their  resistance  is  not  constant. 

§  9.  All  these  defects  are  remedied  in  the  two  fluid  bat- 
teries, of  which  the  DanielVs  cell  was  the  first  invented,  and 
is  a  good  typical  example.  In  the  most  constant  form  of 
this  cell,  the  zinc  is  plunged  in  a  semi-saturated  solution 
of  sulphate  of  zinc,  the  copper  in  a  saturated  solution  of 
sulphate  of  copper,  and  these  two  solutions  are  separated 

FIG.  107. 


either  by  a  porous  earthenware  barrier  or  by  taking  advan- 
tage of  the  different  specific  gravities  of  the  two  solutions. 
Fig.  107  shows  three  Daniell's  arranged  with  porous  cells, 
as  used  in  telegraphy.  The  glass  trough  A  A  has  glass 


222 


Electricity  and  Magnetism.        [CHAP.  XV. 


FIG.  108. 


partitions  B  B,  which  separate  it  into  distinct  cells,  insulated 
from  one  another.  In  these  cells  stand  the  porous  earthen  • 
ware  pots  E  E  E,  containing  a  saturated  solution  of  sul- 
phate of  copper,  and  sur- 
rounded by  a  semi-satu- 
rated solution  of  sulphate 
of  zinc.  A  thick  plate 
of  zinc  is  joined  by  a 
connecting  strap  to  a 
thin  plate  of  copper  at 
D  D  ;  the  coppers  stand 
in  the  porous  cells,  the 
zincs  in  the  sulphate  of 
zinc.  The  terminal  plate 
of  copper  c  forms  the 
positive  pole  of  the  bat- 
tery, and  the  terminal 
zinc  z  has  a  copper  wire 
soldered  to  it,  which 
forms  the  negative  pole. 
In  one  common  form, 
called  Muirheads,  and 
shown  in  Fig.  108,  the 
glass  trough  A  A  contains 
ten  cells,  which  stand 
inside  a  teak  case  with  a 
lid",  through  which  gutta- 
percha-covered  wires 
pass  at  the  ends.  Crys- 
tals of  sulphate  of  copper 
of  the  size  of  a  hazei 
nut  are  placed  in  tht 
porous  cells  to  maintain 
the  solution  in  a  satu- 
rated condition.  The  copper  connecting  strap  is  cast  in  the 
zinc,  having  been  tinned  to  ensure  adhesion.  The  plates 


CHAP.  XV.]  Galvanic  Batteries.  223 

may  be  four  inches  long,  and  two  inches  wide,  and  the 
copper  plates  about  four  square  inches.  The  zinc  should 
hang  on  the  upper  part  of  the  cell,  and  not  reach  to  the 
bottom. 

§  10.  The  chemical  action  in  the  Daniell's  cell  when  in 
perfect  working  order  has  already  been  described,  chap.  xi. 
§9;  the  result  of  the  series  of  actions  there  described  is 
that  the  sulphuric  acid  and  oxygen  of  the  sulphate  of  zinc 
are  transmitted  to  the  zinc,  combine  with  it,  and  form  fresh 
sulphate  of  zinc  ;  the  sulphuric  acid  and  oxygen  of  the  sul- 
phate of  copper  are  transmitted  to  the  zinc,  set  free  by  the 
above  process,  and  reconvert  it  into  sulphate  of  zinc ;  the 
copper  of  the  sulphate  of  copper  is  transmitted  to  the  copper 
electrode,  and  remains  adhering  to  it  The  whole  result 
is  therefore  the  substitution  of  a  certain  quantity  of  sul- 
phate of  zinc  for  an  equivalent  quantity  of  sulphate  of 
copper,  together  with  a  deposition  of  copper  on  the  copper 
or  negative  electrode.  Sulphuric  acid  and  oxygen  have  a 
stronger  affinity  for  zinc  than  for  copper,  otherwise  there 
would  be  no  source  of  power  in  the  substitution. 

The  result  differs  in  two  material  respects  from  that  given 
by  single  fluid  batteries,  i.  No  free  hydrogen  appears  at  the 
copper  electrode.  It  is  impossible  to  say  whether  water  is 
or  is  not  decomposed  at  some  stage  of  the  process,  but  if 
it  is,  the  oxygen  and  hydrogen  recombine  without  becoming 
visible.  In  the  single  fluid  batteries  described,  the  oxygen 
of  the  decomposed  water  combines  with  the  zinc  or  other 
electropositive  metal,  leaving  the  equivalent  of  hydrogen 
free.  In  the  Daniell's  cell  no  oxygen  is  required  from  the 
water,  the  supply  coming  from  the  sulphate  of  copper. 
Consequently  no  free  hydrogen  appears.  2.  It  is  com- 
paratively easy  to  keep  the  solutions  in  a  sensibly  constant 
condition.  The  sulphate  of  copper  solution  is  maintained 
by  the  presence  of  crystals  of  sulphate  of  copper.  The 
sulphate  of  zinc  solution,  if  it  be  saturated  in  the  first 
instance,  simply  deposits  the  sulphate  of  zinc  which  is 
formed.  Practically  it  is  found  better  to  work  with  serai- 


224  Electricity  and  Magnetism.        [CHAP.  XV. 

saturated  solution  of  zinc,  because  a  crust  of  sulphate  of  zinc 
crystals  forms  at  the  edge  of  the  saturated  solution  and  this 
impairs  the  action  of  the  battery  if  it  touches  the  zinc,  and 
injures  the  insulation  of  the  battery  by  forming  a  conducting 
film  all  round  the  edges  of  the  cell,  and  on  the  copper  junc- 
tion straps. 

§  11.  The  Daniell's  cell  will  give  a  constant  electromotive 
force,  and  retain  a  nearly  constant  resistance,  for  weeks  to- 
gether. To  ensure  this  result,  the  following  precautions  must 
be  taken  : 

The  solutions  must  be  inspected  daily  and  kept  in  the  proper 
condition  by  the  addition  of  crystals  of  sulphate  of  copper  and 
the  removal  of  sulphate  of  zinc  solution,  water  being  added 
to  replace  the  liquid  withdrawn.  No  sulphate  of  zinc  or  dirt 
must  be  allowed  to  collect  at  the  lips  of  the  cells.  The  zinc 
plate  must  not  touch  the  porous  cell,  or  copper  will  be 
deposited  upon  it,  which  will  set  up  local  action.  The 
sulphate  of  copper  must  be  free  from  iron.  To  detect 
iron,  add  liquid  ammonia  to  the  solution ;  both  copper  and 
iron  will  be  at  first  precipitated,  making  the  solution  appear 
cloudy;  but  as  more  ammonia  is  added  the  copper  will  be 
redissolved,  forming  a  bright  blue  solution,  and  leaving  the 
iron  as  a  brown  powder.  No  acid  should  be  used  to  set 
the  battery  in  action  ;  it  should  be  charged  with  sulphate  of 
zinc  from  the  first  (unless  a  very  low  resistance,  not  con- 
stancy, be  the  object  in  view).  The  plates  should  be  clean. 
Copper  plates,  if  dirty,  may  be  cleaned  by  being  made  red 
hot,  and  dipped  in  weak  ammonia.  The  card  used  in 
cotton  factories  is  a  good  brush  for  batteries.  Porous  cells 
must  be  examined  to  see  that  they  are  not  cracked ;  if  set 
aside  for  a  time  after  being  used,  they  must  be  kept  moi?t, 
or  the  crystallization  of  the  sulphate  of  zinc  they  contain 
will  crack  them.  The  solution  of  sulphate  of  copper  must  be 
watched  to  see  that  it  does  not  rise  in  the  porous  cells  so 
high  as  to  overflow  the  edges.  This  action  by  which 
liquid  is  drawn  from  one  side  <?f  the  porous  diaphragm  to 


CHAP.  XV.] 


Galvanic  Batteries. 


225 


the  other  is  called  osmose.  The  resistance  of  the  cell 
described  above  with  very  porous  Wedgwood  pots  may 
perhaps  not  exceed  4  ohms;  6  or  10  ohms  is  a  much 
more  common  resistance. 

§  12.  The  various  constructions  of  Daniell's  cell  are  very 
numerous.  When  the  cells  are  large,  a  separate  glass  or 
earthenware  jar  is  generally  used  for  each  cell.  The  porous 
cells  are  cylindrical,  and  the  zincs  and  coppers  are  likewise 
parts  of  cylinders.  Sometimes  the  zincs  and  sometimes 
the  coppers  are  placed  inside  the  porous  cell ;  but  the 
zmc  should  always  be  in  the  largest  receptacle.  Sometimes 


the  copper  electrode  is  made,  the  jar  to  hold  the  sulphate 
of  copper,  the  zinc  being  then  inside  the  porous  cell.  This 
form  of  cell  cannot  be  recommended,  as  the  copper  is  fre- 
quently eaten  away  at  the  corners  and  allows  the  liquids  to 
run  out. 

A  more  distinct  form  of  the  DanielPs  cell  is  that  in  which 
the  porous  cell  is  replaced  by  sawdust;  the  copper  lies  at 
the  bottom  of  the  cell  covered  by  crystals  of  sulphate  of 
copper ;  on  this  sawdust  is  placed,  moistened  with  the 
copper  solution  at  the  lower  part  of  the  cell  and  with  the 
zinc  solution  near  the  top  of  the  cell.  On  the  top  of  all  lies 

Q 


226 


Electricity  and  Magnetism.        [CHAP.  XV. 


the  zinc  plate.  This  form  of  battery  was  first  used  by  Sir 
William  Thomson,  who  made  the  lower  coppers  in  the  form  of 
trays,  which  rested  directly  on  the  zinc  of  the  cell  beneath. 
This  form  would  be  very  convenient  for  plates  of  large  size, 
if  the  copper  were  not  occasionally  eaten  through.  This 
defect  he  has  remedied  by  making  the  trays  of  wood  covered 
with  lead,  electrotyped  with  copper  at  the  bottom.  Fig.  109 
shows  three  of  these  square  trays,  in  which  the  zincs  are 
forty-one  centimetres  long  and  broad.  The  trays  are  seven 
centimetres  deep  inside.  The  resistance  of  one  of  these 
cells  is  about  0*2  ohm. 

The  zinc  is  made  in  the  form  of  a  grating  to  allow 
bubbles  of  gas  to  escape,  and  is  supported  on  blocks  of 
wood  w  at  the  corners. 

§  13.  Fig.  no  shows  a  slight  modification  of  the  sawdust 
battery,  commonly  known  as  Menottfs  element*  In  an  earthen- 

FlG.    110. 


ware  or  glass  cell,  a  flat  circular  plate  of  copper  c  is  laid, 
with  a  piece  of  guttapercha-covered  wire  soldered  to  it;  this 
wire  comes  out  of  the  cell  and  forms  the  positive  pole.  The 
copper  is  covered  with  crystals  of  sulphate  of  copper  and 
sawdust  as  above  described,  and  the  zinc  lies  on  the  top. 
A  little  oil  is  sometimes  added  to  prevent  evaporation. 

*  This  element  differs  in  no  respect  from  one  introduced  for  testing 
the  Atlantic  cable,  by  Sir  William  Thomson,  in  1858. 


CHAP.  XV.]  Galvanic  Batteries.  227 

The  cells  are  usually  about  10  centimetres  diameter  inside 
and  12  centimetres  high.  The  metal  plates  are  then  made 
about  8|  centimetres  diameter.  This  form  of  battery  is 
portable,  and  has  a  constant  E.  M.  F.  Its  resistance  is  high, 
being  usually  about  20  ohms  when  in  fair  condition.  It 
is  chiefly  used  for  purposes  connected  with  testing.  The 
sawdust  cells  are  well  adapted  for  use  at  sea,  where  the 
wash  of  the  solution  tends  to  disturb  the  electromotive 
force  and  to  produce  variable  polarization;  for  even  in  a 
Daniell's  cell  there  is  practically  always  some  polarization. 

Gravitation  batteries  are  like  the  Minotti's  with  the 
sawdust  removed.  They  must  be  kept  perfectly  still,  and 
are  found  difficult  to  manage. 

§  14.  The  following  double  fluid  batteries  are  in  practical 
use  : — i.  Marie  Davy's  element,  which  consists  of  a  carbon 
electrode  in  a  paste  of  proto-sulphate  of  mercury  (Hg2so4,) 
and  water  contained  in  a  porous  pot,  and  a  zinc  electrode 
in  dilute  sulphuric  acid,  or  in  sulphate  of  zinc.  The 
chemical  action  is  similar  to  that  of  the  Daniell's  cell; 
sulphate  of  zinc  is  formed,  and  mercury  deposited  at  the 
carbon  electrode. 

The  sulphate  of  mercury  is  apt  to  rise  by  capillary  action 
to  the  junction  of  the  carbon  and  copper;  it  then  attacks 
the  copper  and  destroys  the  continuity  of  the  circuit.  This 
is  prevented  by  filling  the  pores  of  the  charcoal  at  the  top 
with  melted  paraffin ;  the  sulphate  of  mercury  is  expensive, 
but  very  little  mercury  need  be  wasted,  and  it  is  easily 
re-converted  into  proto-sulphate.  This  material  is  poison- 
ous. The  E.  M.  F.  of  this  element  is  about  1*5  volts,  but 
its  resistance  is  greater  than  that  of  a  Daniell's  cell. 

2.  Grove's  cell. — This  well-known  and  very  useful  element 
consists  of  a  platinum  electrode  plunged  in  nitric  acid, 
more  or  less  diluted,  and  a  zinc  electrode  plunged  in  sul- 
phuric acid  diluted  with  about  twelve  parts  of  water :  the 
two  solutions  are  separated  by  a  porous  cell.  The  zinc  is 
converted  into  sulphate  of  zinc,  the  oxygen  required  being 
Q  2 


228  Electricity  and  Magnetism.        [CHAP.  XV. 

obtained  from  the  water ;  the  hydrogen  is  prevented  from 
remaining  free  at  the  platinum  pole  by  forming,  with  the 
nitric  acid,  water  and  hyponitrous  acid  gas.  This  gas  is  in 
part  dissolved,  and  in  part  appears  as  nitrous  fumes.  These 
fumes  are  not  only  disagreeable,  but  poisonous.  The 
electromotive  force  of  this  battery  varies  from  nearly  two 
volts,  when  the  nitric  acid  is  concentrated  and  the  sulphuric 
acid  solution  has  the  specific  gravity  1*136  (20  parts  sulphuric 
acid  in  100  by  weight),  to  1*63  volt,  when  the  nitric  'acid 
solution  has  the  specific  gravity  1*19  (26*3  parts  N2o5  in 
100  solution),  and  the  sulphuric  acid  the  sp.  gr.  1*06  (9  parts 
in  100  by  weight). 

With  the  zinc  in  sulphate  of  zinc,  and  the  nitric  acid 
solution  sp.  gr.  1-33,  the  E.  M.  F.  is  1-67. 

With  the  zinc  in  solution  of  common  salt,  and  nitric  acid 
sp.  gr.  1-33  (45  parts  in  100),  the  E.  M.  F.  is  1-9  volt. 

The  E.  M.  F.  of  this  cell  is  very  high,  but  its  great  merit 
is  its  low  resistance  which  may  with  moderate-sized  cells  be 
reduced  to  \  of  an  ohm.  The  resistance  of  a  cell  con- 
structed as  follows  was  '212  ohm;  area  of  zinc  plate  27-3 
sq.  in.  :  area  of  platinum  plate  13 '8  sq.  in.  ;  sp.  gr.  of  sul- 
phuric acid  1*06;  nitric  acid  26*3  parts  by  weight  in  100 
of  solution.  The  double  E.  M.  F.  is  easily  got  by  doubling 
the  number  of  Daniell's  elements,  but  the  size  of  these 
elements  must  be  immensely  increased  to  reduce  the  resist- 
ance to  that  of  a  small  Grove's  cell. 

3.  Bunsefts  cell. — This  element  is  exactly  similar  to 
Grove's,  except  that  the  platinum  is  replaced  by  porous 
carbon.  In  both  Bunsen's  and  Grove's  cells  the  zinc  must 
always  be  amalgamated,  or  the  local  action  causes  intoler- 
able fumes  and  waste  of  zinc.  The  electromotive  force  of 
Bunsen's  cell  is  rather  greater  than  that  of  Grove  ;  but  the 
resistance  is  also  greater,  and  there  is  occasionally  difficulty 
in  securing  a  good  contact  between  the  carbon  electrode  and 
the  metallic  strap  or  wire  used  to  connect  it  with  the  next 
zinc  or  with  the  terminal  of  the  battery.  The  carbons  are 


7 


V- 


CHAP.  XV.]  Galvanic  Batteries.  229 

specially  prepared  for  all  carbon  batteries,  and  vary  much  in 
quality.  The  upper  part  of  the  carbon  should  be  impregnated 
with  stearine  to  prevent  the  junction  from  being  corroded. 

Faure  puts  the  nitric  acid  inside  the  carbon  pole,  which  is 
made  in  the  form  of  a  bottle  closed  by  a  carbon  stopper. 
The  carbon  performs  the  double  part  of  porous  pot  and 
electrode.  The  nitrous  fumes  rise  inside  the  bottle,  and  by 
their  pressure  assist  in  forcing  the  nitric  acid  through  the 
porous  carbon. 

The  resistance  of  an  ordinary  Bunsen's  element  1 2  centi- 
metres high  with  the  carbon  outside  the  zinc  is  given  by 
Blavier  as  equal  to  from  2  to  3  ohms  when  partially  charged, 
but  to  double  this  amount  after  a  few  hours. 

4.  The  Chromate  of  potassium  element  is  thus  de- 
scribed by  Mr.  Latimer  Clark :  '  Prepare  two  solutions-, 
4  the  first  to  be  made  by  dissolving  2  ounces  of  bichromate  of 
*  potash  in  20  ounces  of  hot  water,  and  when  cold  add  10 
'  ounces  of  sulphuric  acid. '  As  this  addition  will  cause  the 
'  solution  to  become  warm,  it  must  be  allowed  to  cool  before 
'  being  used.  The  second  is  a  saturated  solution  of  common 
'salt.  To  charge  the  battery-  with  these  solutions  the 
'bichromate  solution  must  be  poured  into  the  porous  jar 
'  containing  the  carbon,  until  it  reaches  about  half  an  inch 
'  from  the  top ;  then  pour  the  salt  solution  into  the  outer 
'  vessel  containing  the  zinc  until  it  reaches  the  same  level.' 

The  electromotive  force  is  said  to  be  2  volts. 

The  chlorine  of  the  common  salt  unites  with  the  zinc, 
forming  chloride  of  zinc,  while  at  the  carbon  electrode  the 
sodium  replaces  hydrogen  in  sulphuric  acid,  forming  sul- 
phate of  sodium.  The  nascent  hydrogen  reduces  chromic 
acid  (produced  by  the  action  of  sulphuric  acid  on  the 
bichromate  of  potash),  so  that  sulphate  of  chromium  is 
produced.  In  chemical  notation, 

3Zn;  6NaCl;  6H2SO4;  2CrO3 
;  6H2O;  3Na2SO4;  Cr2(SO4)3. 


230  Electricity  and  Magnetism.         [CHAP.  XV. 

5.  The  Ledanche   battery ;  a  zinc  carbon  element.    The 
zinc  is  plunged   in   a  solution  of  ordinary  commercial  sal 
ammoniac,  and  the  carbon  is  tightly  packed  in  a  porous  pot, 
with  a  mixture  of  peroxide  of  manganese  and  carbon,  in  the 
form  of  a  coarse  powder.      Its  E.  M.  F.  is  about   1*48  volt. 
The  zinc  unites  with  chlorine,  forming   chloride  of  zinc ; 
ammonia  is  set  free   at  the  negative  electrode,  while  the 
nascent  hydrogen  from  the  ammonium  reduces  the  peroxide 
of  manganese  to  sesquioxide.     The   chemical  notation  of 
the  change  is  that  Zn;  2NH4C1;  2MnO2  is  changed  into 
ZnCl2;  H2O;  2NH3;  Mn2O3. 

6.  Mr.  Latimer  Clark's  cell  of  constant  electromotive  force ; 
this  element  has  already  been  described,  Chap.  X.  §  2. 

§  15.  With  all  batteries  it  is  of  the  utmost  importance  that 
during  any  delicate  experiments  the  whole  battery  should  be 
perfectly  insulated,  and  each  cell  perfectly  insulated  from 
its  neighbour.  For  telegraphic  purposes  this  is  less  essential, 
but  it  is  always  desirable.  When  a  battery  gives  no  current 
or  a  much  feebler  current  than  was  expected,  the  following  are 
defects  which  should  be  looked  for:  i,  solutions  exhausted; 
for  instance,  sulphate  of  copper  in  the  Daniell's  cell  entirely 
or  nearly  gone,  leaving  a  colourless  solution ;  2,  terminals 
or  connections  between  the  cells  corroded,  so  that  instead 
of  metallic  contact  we  have  oxides  of  almost  insulating 
resistance  intervening  in  the  circuit ;  3,  cells  empty  or 
nearly  empty;  4,  filaments  of  deposited  metals  stretching 
from  electrode  to  electrode.  Intermittent  currents  are 
sometimes  produced  by  loose  wires  or  a  broken  electrode 
which  alternately  makes  and  breaks  contact  when  shaken. 
Inconstant  currents  are  also  produced  when  batteries  are 
shaken,  unless  they  are  in  first-rate  condition  :  the  motion 
shakes  the  gases  off  the  electrodes,  increasing  temporarily 
the  £.  M.  F. 


CHAP.  XVL]        Measurement  of  Resistance. 


231 


CHAPTER   XVI. 

MEASUREMENT    OF    RESISTANCE. 

§  1.  IN  order  to  measure  a  resistance  we  must  compare  it 
with  a  standard  recognised  as  the  unit  of  resistance.  In 
telegraphy  the  measurement  of  resistance  plays  a  very 
important  part,  regulating  the  choice  of  materials  and  enabling 
the  electrician  to  test  the  quality  of  goods  supplied.  The 
ohm  (Chap.  X.  §  4)  is  the  unit  of  resistance  almost  universally 
adopted  in  this  country.  Multiples  and  submultiples  of  the 
ohm  are  so  arranged  in  boxes  of  resistance  coils  that  any 
given  resistance  from  one  ohm  to  10,000  or  100,000  ohms 
can  be  readily  obtained  for  comparison  with  any  other  resist- 
ance. The  general  arrangement  of  these  boxes  is  shown  in 
the  diagram,  Fig.  in. 

FIG.  in. 


Between  two  terminal  binding  screws  T  and  TJ  secured  on 
a  vulcanite  slab,  are  fixed  a  series  of  brass  junction  pieces, 
a,  b,  c,  d}  each  of  these  is  connected  by  a  resistance  coil  to 
its  neighbour,  as  shown  at  i,  2,  3,  and  4.  A  number  of 
brass  conical  plugs  with  insulating  handles  of  vulcanite  are 
provided,  which  can  be  inserted  between  any  two  successive 


232  Electricity  and  Magnetism.       [CHAP.  XVI. 

junction  pieces,  as  between  T  and  a,  or  a  and  b.  Conical 
holes  are  bored  for  this  purpose  at  the  opening  between  the 
junction  pieces.  When  the  plugs  are  withdrawn,  no  electrical 
connection  exists  between  the  junction  pieces  except  through 
the  coils. 

Let  us  assume  that  the  resistance  of  the  first  coil  is  one 
ohm,  that  of  the  second  two  ohms,  that  of  the  third 
three  ohms,  and  that  of  the  fourth  four  ohms.  Then  if  the 
plugs  are  arranged  as  in  the  figure  the  whole  resistance 
between  T  and  T!  will  be  4  ohms,  because  the  resistance  of 
the  large  metallic  junction  pieces  directly  connected  by 
plugs  would  be  insensible  between  c  and  T.  If  all  the  plugs 

FIG.  112. 


Td .       .OT      .£>  .       .ffT 

r  -•;        ;  ,-:::=i.,:;i:;:;::;:;;C^;,,  ;.:::-;<::;>;.: 


1 0  20 

tnyr^ 

•v  v-- .  ;  -:--:;::;::;::;V>^r:r^ 

:;V: .  ..b::::/i!j!!!!ii=i!=i=fe:s; 


j*»      .CT.    «       .^   .     ft      .(?   .     c       ^  «      d'""*   Ji 


were  withdrawn,  the  resistance  between  T  and  d  would  be 
10  ohms,  and  obviously  by  properly  arranging  the  plugs  we 
could  obtain  any  resistance  from  i  to  10  between  T  and  d. 
Now  suppose  that  d,  instead  of  being  the  final  terminal 
of  the  set  of  resistance  coils,  were  connected  by  a  thick 
copper  bar  to  /  as  in  Fig.  112,  showing  a  plan  of  the 
lid  of  the  box  containing  the  coils ;  and  that  a  similar 
series  of  junction  pieces  were  used  to  connect  coils  of  10, 
20,  30,  and  40  ohms,  precisely  as  a,  b,  ct  and  d  connected 
the  coils  i,  2,  3,  and  4;  then  between  /  and  d^  if  all  the 


CHAP.  XVI.]       Measurement  of  Resistance.  233 

plugs  were  out,  we  should  have  a  resistance  of  100  units, 
but  by  inserting  the  proper  plugs  we  could  at  will  have  10, 
20,  30,  40,  50,  60,  70,  80,  or  90  units.  Thus  for  80  units, 
withdraw  the  ist,  3rd,  and  4th  plug,  giving  10  +  30  +  40  or 
80  units.  •  Now  between  dl  and  x  we  can  obviously  by  proper 
plugging  obtain  any  number  of  units  between  i  and  1 10  ;  dl 
is  connected  by  a  thick  bar  with  tl9  the  last  of  five  junction 
pieces  joining  coils  of  100,  200,  300,  and  400  units,  by  means 
of  which,  between  d\  l  and  T,  we  can  get  with  the  twelve  plugs 
any  number  of  units  from  i  to  mo;  similarly  with  four 
more  junction  pieces  and  four  more  coils  we  have  between 
T!  and  T,  the  final  terminals  of  the  box,  a  series  of  sixteen 
coils  and  sixteen  plugs,  by  the  proper  arrangement  of  which 
we  can  between  T  and  TT  obtain  any  number  of  units  of  re- 
sistance from  i  to  ii  1 10  ;  when  all  the  plugs  are  in  their 
places  the  resistance  between  T  and  i^  ought  to  be  very  small 
relatively  to  the  resistance  of  one  ohm ;  and,  if  this  is  not 
the  case,  the  plugs  and  holes  must  be  well  cleaned,  as  any 
resistance  observed  when  all  the  plugs  are  in,  can  only  be 
due  to  imperfect  metallic  contact  between  the  holes  and  plugs. 

§  2.  Many  other  arrangements  of  resistance  coils  may  be 
adopted.  Thus,  instead  of  the  i,  2,  3,  4  series,  we  might  have 
had  ten  equal  coils  in  each  row  of  junction  pieces,  but  this 
would  have  required  40  plugs  instead  of  16.  We  might 
also  have  arranged  ten  coils  in,  a  circle,  and  joined  them  to 
ii  equidistant  junction  pieces,  as  in  Fig.  113.  Then  the  re- 
sistance between  the  wires  /  and  t\  would  be  2  if  the  arm  A 
was  on  the  second  stop,  or  5  if  on  the  fifth  stop.  The 
end  of  the  arm  A  may  be  so  arranged  that,  before  leaving 
one  junction  piece,  it  makes  contact  with  the  next,  so  that 
the  circuit  between  t  and  ^  is  never  wholly  broken. 

In  all  boxes  of  resistance  coils  the  following  precau- 
tions should  be  observed  during  the  manufacture.  Large 
gauges  of  wire  should  be  used  for  the  smaller  coils  instead 
of  short  pieces  of  fine  wire.  Better  adjustment  and  less 
liability  to  derangement  by  a  powerful  current  is  thus  ob- 


234  Electricity  and  Magnetism.      [CHAP.  XVI. 

tained.  The  metal  used  for  the  wire  must  be  such  that  its. 
resistance  varies  little  with  changes  of  temperature.  German 
silver  is  a  good  material.  The  wires  should  be  insulated  with 

FIG.  113. 


FIG.  114. 


two  coatings  of  silk  saturated  with  solid  paraffin  or  other 

suitable  insulating  mixture.  No  solderings  should  be  per- 
mitted inside  the  coils — above  all,  no 
solderings  in  making  which  acid  is  used. 
The  wire  should  be  wound  double,  so 
that  the  current  makes  as  many  turns  from 
left  to  right  as  from  right  to  left.  There  is 
no  self-induction  (Chap.  III.  §  21)  in  a  coil 
so  wound,  nor  does  the  current  affect  gal- 
vanometers in  the  neighbourhood.  The 
junction  pieces  must  be  firmly  fixed,  well 
insulated,  and  so  formed  that  the  vulcanite 
on  which  they  stand  can  be  easily  cleaned. 
It  is  a  good  plan  to  make  the  bobbins 
hollow,  and  rather  of  large  than  small 

diameter,  to  promote  uniformity  of  temperature.     All  the 

bobbins  should  be  in  one  box. 


•pHAp.  XVI.]       Measurement  of  Resistance.  235 

If  §  3.  Let  two  points  A  and  B,  Fig.  114,  be  joined  by  two 
conductors  having  resistances  r  and  rlt  these  conductors 
are  said  to  be  joined  in  multifile  arc ;  with  a  difference  of 
potentials  1  between  A  and  B. 

The  current  c  through  r  will  be  equal  to  -,  and    similarly 

the  current  through  rl  will  be  —  ;  the   whole    current  be- 

r\ 

tween  A  and  B  will  be  -  +  — ,  or  1  ^l  +  r> ;  this  current  will 
r       rl  rr} 

be  the  same  as  if  A  and  B  had  been  joined  by  a  single  re- 
sistance equal  to   .   rr}    ,  which  is  therefore  the  resistance  of 
r  +  rf 

the  two  conductors  joined  in  multiple  arc.     With  three  wires 
r>  M>  riu  connecting  the  same  points  by  a  multiple  arc,  the 


i  MI 


resistance  between  A  and  B  will  be    

r  rl  +  M  rn  +  r  ru 

If  a  galvanometer  with  the  resistance  G  be  shunted  by  a 
shunt  of  the  resistance  s,  the  resistance  of  the  shunted  galvano- 

"   meter  will  be      G  s   .     Let  u  =  5-Jlf,  then  the  sensibility 

G   +    5  S 

of  the   shunted   galvanometer  will   be   to  that  of  the  un- 
shunted  galvanometer  as  1  to  u ;  then  calling  c  the  current 

flowing  in  other  parts  of  the  circuit,  -   will   flow    through 

the  galvanometer,  and  — c  will  flow  through  the  shunt ;  the 
us 

resistance  of  the  shunted  galvanometer  will  be  -. 

Example. — We  have  a  galvanometer  with  a  resistance  of 
8,000  ohms,  and  wish  to  find  the  shunt  which  will  reduce  its 

sensibility  100  fold,  u  =  100  =  8_i^_±_f  or  s  =  8;0°°  = 

s  99 

80-8. 

The  resistance  of  the  galvanometer  when  shunted  will  be 
^     _   8, coo 
u 


236  Electricity  and  Magnetism.      [CHAP.  XVI. 

§  4.  Definition. — The  conductivity  of  a  given  wire  or  con- 
ductor is  the  reciprocal  of  its  resistance. , 

That  is  to  say,  if  a  be  the  resistance  of  the  wire,  —  is  its 

a 

conductivity ;  if  the  resistance  of  a  conductor  is  TO  ohms, 
its  conductivity  is  0*1. 

The  conductivity  of  a  number  of  wires  joining  two  points 
in  multiple  arc  is  the  sum  of  the  conductivities  of  the  several 
wires.  For  the  current  in  each  wire  with  a  unit  differ- 
ence of  potential  between  the  ends  is  -. 

The  sum  of  all  the  currents  is 

1  +  I  +  i_  +       l 

I         •     •      •      • —  9 

r        r\        rn  m 

which  is  the  same  current  as  if  a  single  conductor  joined 

the  two  points  with  a  conductivity  of  (-+  —  +  —  .  .  .  +  — ) 

V      ^      rn  rj 

The  resistance  of  the  wires  in  multiple  arc  is  the  reciprocal  of 
the  conductivity  of  the  multiple  arc.  This  rule  gives  the 
same  expression  for  the  resistance  as  is  given  in  §  3. 

Example. — Let  two  points  be  joined  by  wires  in  multiple 
arc  with  resistances  of  2,  18,  27,  and  64  ohms  respectively. 

The  conductivities  are  0*5,  0*05555,  "°37°4>  '01562.  The 
sum  of  the  conductivities  is  0*6082  ;  and  the  resistance  of 

the  four  wires  in  multiple  arc  =  — =  1*644  ohms. 

•6082 

§  5.  We  may  compare  one  resistance  with  another  by 
comparing  the  deflections  produced  by  a  given  battery 
through  the  same  galvanometer,  but  with  the  different 
resistances  in  circuit.  Thus,  let  G  be  the  galvanometer 
resistance,  B  the  battery  resistance,  R  a  resistance  chosen  at 
pleasure  from  those  at  our  disposal  in  the  box  of  resistance 
coils,  and  x  the  unknown  resistance  which  we  wish  to  measure 
or  compare  with  R.  Let  us  first  observe  the  deflection  d  ob- 
tained with  a  circuit  containing  G,  B,  and  R  only,  arranged  in 


CHAP.  XVI.]      Measurement  of  Resistance,  237 

any  order,  and  next  the  deflection  d^  obtained  with  G,  B,  and 
x  only  in  circuit  :  then,  if  the  galvanometer  be  a  mirror 
galvanometer,  the  deflections  of  which  are  proportional  to  the 
currents  flowing  through  it,  we  have,  by  Ohm's  law,  the  pro- 
portion 

G  +  B  +  R:G  +  B  +  A:  =  </I    :    d-} 
for  the  E.  M.  F.  being  the  same  in  both  cases,  the  currents  and 
therefore  the  deflections  must  be  inversely  proportional  to 
the  total  resistances.     From  the  above  we  find 

x  =  1L  (G  +  B  +  R)  -  (G  +  B)  .  .  .  1°. 

»i 
When  G  and  B  are  so  small  that  they  can  be  neglected 

relatively  to  R,  we  have  approximately  x  =  —  -  R.    This  case 

tf, 

seldom  arises  ;  but  frequently,  as,  for  instance,  when  x  is  the 
resistance  of  some  insulating  substance,  we  may  neglect 
G  -j-  B  as  insensible  relatively  to  x,  and  then  we  have 


The  number  d  (G  +  B  +  R)  is  in  telegraphy  called  the  con- 
stant vi  the  instrument  with  the  given  battery.  If^/1  =  l,  we 
shall  have  the  whole  resistance  of  the  circuit  x  =  d(c  +  B 
4-  R)  ;  hence  the  constant  is  often  defined  as  the  resistance 
of  the  circuit  with  which  the  given  battery  would  give  the 
deflection  1.  Obviously  when  a  tangent  galvanometer  is 
used,  we  must  write  tan  d  and  tan  dl  in  the  above  formulae 
instead  of  d  and  dl  ;  and  if  a  sine  galvanometer  is  used, 
we  must  write  sin  */and  sin  dv 

\/  §  6.  By  the  use  of  shunts  the  application  of  this  method 
is  greatly  extended;  calling  the  resistance  of  the  shunt 
s,  the  resistance  of  the  shunted  galvanometer  becomes 

-  ;  hence  if  the  shunt  be  used  when  both  d  and  </,  are 


observed,  we  must  in   equation   1   substitute  -^-   for  G, 

G  +  S 


238  Electricity  and  Magnetism.      [CHAP.  xvi. 

the  only  effect  being  to  diminish  the  resistance  of  the  galva- 
nometer ;  but  when  d  is  observed  with  the  shunt  in,  and  d\ 
without  the  shunt,  the  sensibility  is  different  in  the  two  cases. 

Then  let  the  ratio  be  called  u  as  before ;  we  have  by 
Ohm's  law  : — 

-    +B  +  R    \   G  +  B  +  #  =  //,    :    u  d. 
u 

or  x  -=  //  p  /-  +  B  +  R)  -  (G  +  B)   ...  3°. 

The  constant  of  the  unshunted  galvanometer  of  resistance 
for  which  d^  =  1,  is  u  d  (-  +  B  +  R). 

Thus  with  a  shunt  reducing  the  sensibility  loo-fold,  a 
deflection  of  90  divisions,  with  G  =  8000,  B  =  20,  and 
R  =  4000,  the  constant  will  be  36,900,000  ;  this  will  be  the 
whole  resistance  of  the  circuit  including  G  and  B  with  which 
the  battery  used  would  give  the  deflection  1  on  the  galvano- 
meter used  without  a  shunt  In  practice  R  is  chosen  so  that 

-  +  B  +  R  may  be  some  whole  convenient  number ;  thus 

in  the  above  case  an  experienced  observer  would  have  made 
R  =  3900  when  the  constant  would  have  been  36,000.000. 
A  series  of  shunts  are  usually  sold  with  each  galvanometer  of 
such  resistance  that  u  may  by  them  be  made  10,  or  100,  or 
1000  at  pleasure.  The  constant  is  determined  at  the 
beginning  of  the  experiment  when  the  galvanometer  is  not 
shunted,  and  the  value  of  the  resistance  in  circuit  giving  a 
deflection  d\  is  obtained  by  simply  dividing  u  times  the 
constant  by  dv  To  get  x,  the  resistance  of  G  +  B  must 
be  subtracted  from  the  whole  circuit,  but  when  the  sum  of 
G  +  B  is  small,  this  subtraction  is  often  omitted. 

This  mode  of  measuring  a  resistance  is  much  used  in  test- 
ing insulating  materials,  such  as  gutta-percha.  The  battery 
and  wire  covered  with  gutta-percha  are  arranged  as  in  Fig. 


FIG.  115. 


CHAP.  XVI.]      Measurement  of  Resistance.  239 

The  negative  current  flows  from  z  through  the  shunted 
galvanometer  to  the  copper  wire  inside  the  gutta-percha ; 
then  through  the  gutta-percha  to  the 
water  in  the  tub  T,  and  from  T  to  the 
copper  pole  of  the  battery.  The  resistance 
x  is  the  resistance  of  the  gutta-percha. 

§  7.  The  value  of  R  in  the  above  equa- 
tions is  always  known,  and  the  value  of  G 

or  of  -  is  also  generally  known,  and  can 

always  be  directly  determined  by  experi- 
ment ;  for  instance,  it  may  be  measured  as 
any  other  resistance  would  be  measured, 
a  second  galvanometer  being  used  for  the 
purpose.  The  value  of  B  should  be  de- 
termined at  least  once  a  day,  since  the 
resistance  of  any  battery  is  found  to  vary 
considerably  from  day  to  day.  There  are 
several  methods  of  determining  the  value 
of  B.  The  following  is  the  most  com- 
mon : — 

"Make  a  circuit  consisting  of  the  battery  B,  the  galvano- 
meter G,  and  a  set  of  resistance  coils  R ;  shunt  the  galvano- 
meter with  a  piece  of  short  thick  wire  connecting  the  ter- 
minals ;  put  all  the  plugs  of  the  resistance  coils  in  their 
places  so  as  to  reduce  R  sensibly  to  zero  ;  let  the  wire  shunt 
be  so  short  and  thick  as  to  have  no  sensible  resistance 
relatively  to  the  battery,  but  adjust  it  of  such  length  that  a 
sensible  deflection  D  is  shown  by  the  galvanometer ;  the 
greater  part  of  the  current  is  shunted,  but  enough  goes 
through  the  sensitive  galvanometer  to  give  the  deflection 
D  ;  under  these  circumstances  the  whole  resistance  of  the 
circuit  is  B,  that  of  the  battery,  for  R  is  reduced  to  nothing, 
and  the  resistance  of  the  shunt  is  insensible  ;  now  increase 
the  resistance  in  the  box  to  R  by  taking  out  plugs  until  a 
deflection  DJ  is  obtained  ;  then 


T" 


240  Electricity  and  Magnetism.       [CHAP.  XVI. 

R  -f  B   :   B  =  D  :  D,,  or  B  =  -5-5 !-      ....  4° 

D  —  D! 

If  D  i  =  —  we  have  B  =  R 

2 

This  method  has  the  defect  that  the  battery  resistance  is 
measured  when  a  powerful  current  is  passing,  increasing  the 
polarization.  Moreover  the  current  is  very  different  when 
D  and  Dt  are  taken,  and  the  polarization  very  different. 
Consequently  Ohm's  law  is  seldom  strictly  applicable,  be- 
cause the  E.  M.  F.  of  the  battery  is  not  strictly  constant 
throughout  the  experiment.  With  a  battery  of  very  small 
resistance,  this  method  would  be  liable  to  injure  the  re- 
sistance coils. 

The  following  is  a  second  method  by  which  the  sum 
B  -f-  G  is  determined.  Observe  two  deflections  D  and  DJ 
given  by  the  battery  when  the  two  circuits  are  B  +  G  -f  R 
and  B  +  G  +  R!  ;  then  we  have  G  +  B  +  R  :  G  +  B  +  Rt 
=  D,  :  D,  and 


B  = 


D  —  D! 

Mr.  Varley  recommends  that  three  deflections  D,  D1?  and 
DU,  be  taken  with  additional  resistance  R,  R1?  and  Rn  for 
the  purpose  of  testing  whether  polarization  interferes  much 
with  the  experiment;  if  there  be  no  polarization,  adjusting 
the  values  of  R,  R1;  and  Rn  so  that  DH  =  40  and  D,  —  2 
D,  we  should  have  R  =  3  R!  —  2  Ru. 

The  following  is  a  third  method.  Arrange  the  connec- 
tions as  in  Fig.  116;  let  D  be  the  deflection  when  the  cir- 
cuit is  B  +  R  +  G  ;  next  insert  the  shunt  of  known  resistance 
s,  by  making  con  tact  at  #  ;  reduce  R  to  R!  until  the  deflec- 
tion is  the  same  as  before,  then 

B  =  SR  -  Rl.        .   6° 
G  +  R! 

or,  fourthly,  leaving  R  unaltered,  let  D,  be  the  deflection 
observed  when  contact  is  made  at  a  \  then 


CHAP.  XVI.]       Measurement  of  Resistance. 


24 1 


D    —    D, 


B  =  S 


D,  —  D   — 


or  approximately 


.  8C 


This  method  is  especially  applicable  to  batteries  of  very 
small  resistance. 

§  8.  The  accuracy  with  which  a  resistance  can  be  mea- 
sured by  any  of  the  above  methods  is  limited  by  the  accu- 
racy with  which  a  deflection  can  be  observed.  If  we  cannot 
make  certain  that  any-  deflection  is  correct  within  one  per 
cent,  still  less  can  we  feel  confident  that  the  resistance 
calculated  from  the  deflection  is  correct  within  one  per  cent. 

FIG.  116.  FIG.  117. 


The  following  methods,  which  may  all  be  termed  differential 
methods,  admit  of  much  greater  accuracy.  The  simplest 
differential  method  has  already  been  described  (Chap.  IV. 
§  3),  and  the  arrangement  of  the  connections  is  shown  in  Fig. 
117.  With  a  sensitive  galvanometer  it  admits  of  extreme 
accuracy,  for  by  increasing  the  battery  power  we  may  increase 
at  pleasure  the  deflection  which  the  difference  between  the 

R 


242  Electricity  and  Magnetism.      [CHAP.  XVI. 

currents  in  the  two  branches  produces.  We  may  also  shunt 
either  branch  of  the  galvanometer  so  as  to  reduce  its  resist- 
ance and  sensibility  u  times.  Calling  the  resistance  of  each 
branch  of  the  instrument  G,  we  then  have,  when  the  galvano- 
meter is  undeflected  on  completing  the  circuit,  assuming  that 
the  known  resistance  is  connected  with  the  shunted  branch 
of  the  galvanometer, 

R  +  -  :  x  +  G  =  i  :  u 
u 

or  x  =  u  R  .  .  .  .  9° 
If,  as  in  the  figure,  x  is  connected  with  the  shunted  branch 

we  have  x   =  - . 
& 

Resistances  one  thousand  times  greater  or  one  thousand 
times  less  than  R,  are  easily  measured  in  this  way.  In  order 
that  the  plan  should  give  accurate  results,  it  is  necessary  that 
the  ratio  u  be  accurately  known  and  that  it  remain  constant. 

p  I  q 

Now  u  =  —     — ;  and  if  the  resistance  of  either  G  or  s  varies 

during  the  experiment  fallacious  results  are  given. 

When  the  wire  of  a  differential  galvanometer  is  made  of 
copper  the  shunts  must  be  of  copper  also,  in  order  that  the 
ratio  u  may  be  constant  at  all  temperatures;  but  even 
with  this  precaution,  the  very  current  employed  in  testing 
disturbs  the  value  of  u,  for  a  much  larger  current  flows 
through  s  than  through  G,  and  hence  more  heat  is  generated 
in  the  shunt  than  in  the  galvanometer  coil,  and  this  heat  is 
concentrated  in  a  comparatively  small  mass  of  metal ;  the 
consequence  is  that  the  resistance  of  the  shunt  is  increased 
relatively  to  that  of  the  galvanometer  by  every  current 
which  passes,  and  this  seriously  impairs  the  value  of  the 
method.  Diffeiential  galvanometers  made  of  German 
silver  give  much  more  accurate  results  than  copper  wire 
instruments,  because  their  resistance  and  that  of  their  shunts 
are  less  affected  by  temperature.  The  circuit  should  be  com- 
pleted for  the  shortest  possible  time  by  making  contact  with 


CHAP.  XVI.]       Measurement  of  Resistance.  243 

a  key  at  #,  and  breaking  it  as  soon  as  a  deflection  to  right  or 
left  has  been  observed.  This  may,  however,  lead  to  error  if 
the  unknown  resistance  x  is  so  formed  that  any  self-induction 
can  take  place,  or  if  x  has  any  sensible  electrostatic  capacity 
like  a  gutta-percha-co.vered  wire  in  water.  In  either  of  these 
cases  the  currents  in  the  two  branches  will  not  increase  at 
the  same  rate  when  contact  is  first  made.  Assuming  the  coils 
in  R  to  be  properly  wound,  while  x  is  a  simple  bobbin  of 
wire  not  wound  double,  the  current  in  x  will  lag  behind, 
and  hence  a  momentary  contact  at  a  will  always  show  x  as 
greater  than  R  when  it  is  really  equal  to  it.  The  first  jerk 
of  the  galvanometer  needle  must,  in  this  case,  be  neglected, 
and  x  measured  by  means  of  the  permanent  deflection 
arrived  at  after  the  currents  in  the  various  branches  have 
become  constant. 

§  9.  When  a  steady  current  c  through  a  resistance  R  is 
due  to  a  difference  of  potentials  i  between  the  ends  of  the 
conductor,  then  the  difference  of  potentials  /  between  any 
two  intermediate  points  separated  by  a  resistance  r  must  be 
equal,  by  Ohm's  law,  to  r  c ;  the  smaller  the  resistance  be- 
tween the  two  points  the  less  the  difference  of  potential 
between  them,  and  if  one  end  of  the  conductor  be  at  zero 
potential  or  uninsulated,  the  potential  of  any  point  in  the  con- 
ductor will  be  proportional  to  the  resistance  r  between  the 
earth  and  the  point  in  question,  and  equal  to  r  c.  In  the 
diagram  Fig.  118,  if  the  line  A  E  represents  to  any  scale  the 
FIG.  1 1 8. 


length  of  a  uniform  conductor  separating  the  battery  c  z 
from  the  earth  at  E,  and  if  the  line  or  ordinate  p  A  represent 
the  E.  M.  F.  of  the  battery  to  any  scale  :  then,  joining  p  E  by 
a  straight  line,  the  ordinate  F  H  will  represent  the  potential 


244  Electricity  and  Magnetism.      [CHAP.  XVI. 

of  the  conductor  at  the  point  F.  If,  for  instance,  p  A  is 
equal  to  1 2  volts,  and  F  is  half-way  between  A  and  E,  F  H 
will  be  equal  to  6,  and  6  volts  will  be  the  potential  of  the 
conductor  at  that  point. 

If  A  were  separated  from  E  by  several  conductors  of  dif- 
ferent resistances,  we  must  draw  A  E  so  as  to  represent  the 
total  resistance  instead  of  the  mere  length  of  the  conductor. 
Then  as  before,  F  H  will  represent  the  potential  at  the  point 
F,  separated  from  E  by  a  resistance  equal  to  F  E  ;  if  F  is  so 
placed  that  the  resistance  of  F  E  is  equal  to  that  of  A  F,  the 
potential  at  F  will  be  half  that  at  A,  in  whatever  manner 
the  resistances  A  F  and  F  E  are  made  up. 

The  difference  of  potential  between  B  and  F  is  equal  to 
the  difference  of  the  length  of  the  lines  B  D  and  F  H. 

Let  us  now  suppose  that  the  two  ends  of  the  resistance 
A  D  B  are  joined  to  the  two  poles  of  an  insulated  battery, 
and  that  at  the  middle  of  the  resistance  at  D  the  conductor 
is  connected  with  earth,  Fig.  119.  The  potential  here  will  be 
zero;  but  the  difference  of  potentials  between  A  and  B  must  be 

FIG.  119. 
P\ 


equal  to  nearly  the  whole  E.  M.  F.  of  the  battery,  assuming  the 
resistance  between  A  and  B  to  be  large  relatively  to  that  of  the 
battery.  Hence  A  P!  will  be  equal  to  half  that  E.  M.  F.,  and 
B  PU,  a  negative  ordinate,  will  be  equal  to  the  same  quantity. 
The  sum  of  the  lengths  B  Pn  +  A  Pl  =  A  P,  calling  A  p  the 
E.  M.  F.  of  the  whole  battery  as  shown  in  Fig.  118.  The 
ordinates  F  H  and  FJ  H!  show  the  potentials  at  points  F 
and  FI,  one  positive  or  measured  upwards,  the  other  nega- 
tive or  measured  downwards.  The  difference  of  potentials 
between  F  and  Ft  "is  the  sum  of  H  F  and  HJ  Fr  This  differ- 


CHAP.  XVI.]      Measurement  of  Resistance.  245 

ence  will  be  exactly  the  same  whatever  point  of  A  B  be  put  to 
earth,  if  the  battery  is  insulated.  If  FI  were  put  to  earth 
instead  of  D,'  then/!/u  would  be  the  line  showing  the 
potentials,  and  F  h,  the  difference  of  potentials  between  F 
and  FU  is  equal  to  F  H  -f  Fl  H^ 

§  10.  Let  us  assume  that  the  same  difference  of  potentials 
is  maintained  by  a  battery  between  the  ends  of  two  con- 
ductors of  different  resistance  represented  by  the  lines  A  E 
and  AJ  E1?  Fig.  120,  and  for  simplicity's  sake  we  will  further 
assume  that  the  potential  at  E  is  zero.  If  we  now  choose  any 
two  points  B  and  BJ  so  placed  that  A  B  I  B  E  =  AJ  BJ  I  EI  Eb 
we  shall  have  the  line  B  D  equal  to  BJ  DJ,  showing  that  the 
potentials  of  B  and  Bt  are  equal.  Hence,  if  we  join  B  and 
El  by  a  conductor,  no  current  will  flow  from  B  to  Bt ;  and  if 
a  galvanometer  owere  inserted  in  the  wire  joining  B  and  B,, 
it  would  remain  undeflected,  although  the  E.  M.  F.  represented 
by  AP  and  producing  the  currents  through  AEandAj  Et 
might  be  very  great  and  the  galvanometer  very  sensitive. 
If,  however,  the  wire  or  bridge,  as  it  is  called,  joins  B  with 
a  point  in  A}  EI  between  B,  and  E},  we  shall  have  a  current 
from  A  E  which  runs  through  the  bridge  ;  and  on  the  contrary, 
if  the  bridge  joins  B  with  a  point  between  vl  and  A19  the 

FIG.  120. 


current  will  flow  in  the  opposite  direction  through  the  gal- 
vanometer, i.e.  from  AT  E!  through  the  bridge. 

If  then  we  know  the  ratio  A  B  to  B  E,  as  we  shall  do  if 


246  Electricity  and  Magnetism.       [CHAP.  XVI. 

these  two  resistances  are  made  up  of  graduated  resistance 
coils,  we  shall  be  able  to  divide  a  resistance  AT  E!  in  the 
same  ratio  by  simply  seeking  the  point  BJ  at  which  no 
current  flows  across  the  bridge. 

And  if  A!  BJ  is  a  known  resistance,  we  can  experimentally 
find  a  resistance  SIEI  which  shall  bear  the  same  ratio  to 
A}  B!  as  B  E  does  to  A  B. 

§  11.  The  principles  laid  down  in  the  two  preceding 
sections  give  the  most  convenient  method  of  measuring 
resistance.  The  Bridge,  as  it  is  technically  called,  is  ar- 
ranged as  in  Fig.  121. 

Four  conductors,  A  B,  BE,  A  Bl5  and  El  E,  are  joined  at  A 
and  E  to  the  poles  of  a  battery,  the  current  from  which 
flows  round  ABE  and  AB^,  corresponding  to  ABE  and 
A!  B!  E!  in  Fig.  120.  The  difference  of  potentials  between  A 
and  E  depends  on  the  battery  used,  but  is  obviously  the 
same  for  the  ends  of  the  two  circuits.  The  resistance  be- 
tween A  and  B  we  will  call  R;  that  between  A  and  Bl5  R!  ; 
that  between  B  and  E,  r ;  and  that  between  EI  and  E,  x  the 
unknown  resistance  to  be  measured  ;  R,  RU  and  r  are 
usually  resistance  coils. 

A  convenient  constant  ratio  is  chosen  for  R  and  r>  such 

FIG.  121. 


as  equality,  i  to  10,  i  to  100,  or  i  to  1,000  ;  and  then  EI  is 
adjusted  until  no  current  flows  through  the  galvanometer  G  ; 


CHAP.  XVI.]      Measurement  of  Resistance.  247 

when  this  is  the  case  we  have  R  \  r  =  RI  \  x  or  x  —  —  RI  : 

R 


so  that  if  r  —  — — ,  x  will  be  equal  to  — l-. 
100  100 

The  convenience  of  this  method  is  very  great.  Any  gal- 
vanometer can  be  employed;  but  the  more  sensitive  the 
instrument  the  more  delicate  the  measurement  of  x.  The 
constancy  of  the  resistance  of  the  galvanometer  is  of  no  con- 
sequence. The  coils  R,  Rl3  and  r,  are  made  of  German  silver 
or  some  other  alloy  varying  little  in  resistance  with  a 
change  of  temperature.  Two  keys  are  inserted,  one  at  a  and 
one  at  b  ;  the  current  is  wholly  cut  off  the  four  conductors 
until  contact  is  made  at  a ;  and  then,  after  the  currents  in  the 
four  conductors  have  come  to  their  permanent  condition, 
contact  is  made  at  b  to  test  whether  any  current  flows 
through  the  galvanometer.  If  none  flows,  making  contact 
at  b  does  not  disturb  the  currents  in  the  four  conductors 
at  all.  R  and  r  are  usually  so  arranged  as  to  give  any 
decimal  ratio  between  1,000  to  i  and  i  to  1,000  :  the  two 
keys  at  a  and  b  are  often  arranged  so  that  the  same  finger- 
piece  moves  both,  making  contact  at  b  a  little  after  contact 
has  been  made  at  a. 

The  three  resistances  R,  RJ,  and  r,  and  the  resistance  of 
the  galvanometer,  should  be  small  if  x  is  small,  and  great  if 
x  is  great.  When  x  is  very  small,  A  B  E  is  frequently  made 
of  a  single  wire  of  constant  diameter ;  RJ  is  kept  constant, 
and  the  point  B  slipped  along  the  wire  ABE,  until  no 
current  flows  through  G.  Then  the  ratio  of  the  resistances 

-   is  the  ratio  of  the  actual  lengths    — .   measured   on   a 
R  AE 

scale  over  which  the  wire  ABE  is  stretched.  An  alloy 
of  silver  with  33-4  per  cent,  of  platinum  makes  a  good  wire 
for  this  purpose.  It  must  be  a  stout  wire,  or  else  the  wear 
and  tear  of  shifting  the  contact  piece  B  will  soon  destroy  the 
uniformity  of  its  section  and  therefore  of  its  resistance. 
When  x  is  small,  great  care  is  necessary  to  prevent  the 


248  Electricity  and  Magnetism.      [CHAP.  XVI. 

resistance  of  mere  connections  between  R,  r,  R1}  and  x  from 
being  sensible.  These  connections  may  be  made  of  stout 
copper  rods  %  centimetre  diameter,  and  junctions  made  by 
dipping  the  ends  of  these  rods  in  mercury  cups,  the  ends 
of  the  rods  being  amalgamated. 

The  bridge  is  applied  to  measure  the  resistance  of  the 
gutta-percha  sheath  used  to  insulate  the  conducting  wire  of 
submarine  cables  :  for  this  purpose  E  is  connected  with 
earth,  the  battery  carefully  insulated,  and  the  wire  to  be 
tested  is  connected  with  BJ,  but  insulated  at  the  other 
end  instead  of  being  connected  with  E  ;  the  insulated  wire 
is  submerged  in  an  uninsulated  tank  or  in  the  sea,  and  thus 
the  only  connection  between  BL  and  E  is  through  the  insu- 
lating cover  or  sheath.  The  resistance  of  this  insulating 
cover  is  therefore  the  resistance  x. 

After  the  wires  have  been  arranged  thus  we  can,  by 
joining  the  end  of  the  conducting  wire  with  E,  measure  the 
resistance  of  the  copper  conductor  immediately  before  or 
after  measuring  the  resistance  of  the  insulator. 

When  no  current  flows  across  the  bridge,  the  position 
of  the  battery  and  of  the  galvanometer  may  be  inter- 
changed, and  no  current  will  flow  from  A  to  E  through  the 
galvanometer. 

§  12.  Kirchhojfs  laws. — If  a  number  of  currents  cv  czc3  .  .  .  c»  are 
flowing  some  to  a  point  A  (Fig.  122)  and  some  from  that  point ;  then, 
since  the  whole  quantity  arriving  at  the  point  must  be  equal  to  that  taken 
away,  the  sum  of  all  the  currents  coming  to  the  point  must  be  equal 
to  the  sum  of  those  going  away  from  it :  hence,  calling  the  first  series 
positive  and  the  second  series  negative  currents,  the  algebraic  sum  of  all 
the  currents  must  be  equal  to  zero,  a  result  written  as  follows, 

2  c  =  o, 
the  letter  2  signifying  that  the  sum  of  all  the  values  of  C  are  to  be  taken. 

Let  there  be  several  sources  lx  I2  I3  of  electromotive  force  in  a  circuit 
(Fig.  123),  some  acting  in  onedirection  and  some  in  another,  and  joined  by 
resistances  Ra  Rb  Rc .  Let  the  currents  flowing  through  each  be  C4  CD  Cc . 
Let  the  difference  of  potential  or  E.M.F.  between  the  two  ends  of  R,  be 
Pa  —  A  J  that  between  the  two  ends  of  Rb ,  Pb  -  /b  ;  and  that  between  the 
two  ends  of  Rc ,  Pt  —  J>t . 


CHAP.  XVI.]      Measurement  of  Resistance.  249 

Then  by  Ohm's  law,  C.  Ra  =  P.  —p..  ,  Cb  Rb  =  Pb  —A  ,  Cc  Rc  =  Pc  —  pc 
or  ca  Ra  +  cb  Rb  +  Cc  R,  =  (P.  —  A  +  Pb  —  A  +  PC  —  Pr  )  =  (P.  —  A  ) 


Now  pa  —  ^>c  is  the  difference  of  potentials  produced  by  the  electro- 
motive force  I2  ;  for  however  high  or  low  the  absolute  value  of  the  po- 


tentials  Pa  or  /c  may  be,  by  definition  the  difference  of  potentials  must 
be  equal  to  the  electromotive  force  between  them.  Similarly  Pb  — /a  =  I3, 
and  Pc  -A  =ii: 

hence  I1  +  I2  +  I3  =  C' R,  +Cb  Rb  +C  Rc , 

or  2 1  =  2  c  R        .         .         .         9. 

The  sum  of  all  the  electromotive  forces  is  equal  to  the  sum  of  the 
products  of  each  current  into  the  resistance  which  it  traverses. 

One  obvious  application  of  this  law  of  Kirchhoff's  is  to  those  cases 
in  which  the  electromotive  force  in  a  circuit,  instead  of  being  due  to  a 
certain  difference  of  potentials  produced  at  one  point  of  the  circuit,  as 
by  a  battery,  is  due  to  an  E.M.F.  distributed  throughout  the  length  of  the 
whole  or  part  of  the  conductor,  as  when  the  E.M.F.  is  due  for  instance 
to  electromagnetic  induction,  where  we  only  know  for  each  part  of  the 
circuit  that  the  E.M.F.  is  so  much  per  centimetre  of  length.  We  now 
see  that  we  need  only  add  up  all  the  electromotive  forces  in  each  unit 
of  length,  and  then,  knowing  the  whole  E.M.F.,  we  find  that  the  current 
multiplied  into  the  whole  resistance  of  the  circuit  will  be  equal  to  the 
electromotive  force  thus  calculated — in  other  words,  Ohm's  law  is  per- 
fectly applicable  to  this  case. 

The  results  arrived  at  in  sections  I  and  2  of  this  chapter  are  easily 
proved  from  Kirchhoff's  equations. 


250 


Electricity  and  Magnetism.      [CHAP.  XVI. 


§  13.  The  theory  of  the  bridge  may  be  proved  as  follows 
from  KirchhofFs  laws  : 

Let  five  conductors  r,  ri}  r-A,  rm,  riv,  be  arranged  as  in  Fig. 
1 24  with  a  battery  I  connected  with  A  and  E  by  conductors, 
as  shown  in  the  figure. 

Let  c,  fit  r^  451,  <riv,  c  be  the  six  currents,  in  the  six  parts  of 
the  circuit,  c  being  the  current  in  r,  4  the  current  in  rb  etc. 

Then  at  A  and  E  we  have  c  =  4  +  <rm  =  CA  +  civ 
,,     at  B  and  BJ  ,,      ,,    c  =^  c^  •—  c-A  ^^  c^  ~~   c\^. 

In  the  circuit  A  B  BJ  we  have  c  r  =  c-M  rm  —  ^  r-r 
„  B  E  BJ        „        c  r  =  c-A  r-A  —  civrlv  ; 

eliminating  4  <ru  cm  and  riv  we  have  from  the  above   equa- 
tions : 


This  gives  the  value  of  the  current  produced  in  the  bridge 
r  in  terms  of  the  whole  current  c  produced  by  the  battery. 
If  there  is  no  current  in  r,  we  must  have 

>m  ra  —  r\  r™  =  °  or  r\  •  ra  —  riii  •  riv 
§  14.  The  specific  resistance  of  a  material  referred  to  unit 
of  volume  is  the  resistance  of  the  unit  cube  to  a  current 
FIG.  124. 


between  two  opposed  faces.     The  following  table  contains 
the  specific  resistances  of  several  metals  and  alloys  at  o°  C. 


CHAP.  XVI.]       Measurement  of  Resistance. 


2.51 


The  specific  resistances  given  are  those  of  a  cubic  centi- 
metre of  chemically  pure  metals  calculated  from  experiments 
by  Dr.  Matthiessen.  The  resistances  of  commercial  metals 
are  always  higher,  and  frequently  very  much  higher.  It  is 
not  at  all  uncommon  to  meet  with  copper  having  50  per 
cent,  more  resistance  than  that  in  the  table.  This  is  due  to 

Table.     Specific  Resistance  of  Metals  and  Alloys  at  o°  Centtgi'ade,  from 
Dr.  Matthiessen^  s  experiments. 


gsg  _ 

|l.s 

•  g| 

£«4 

|Jj 

°  £  £  <5 

^  is  -3 

u!  a  J3  jj 

ff  B 

Ciai 

£  *"£ 

jt.9*^ 

^  J2    '^     •*-» 

.—  g 

°  *     S 

O  bB  tj) 

NAMES  OF 

c  tL§U 

METALS. 

JPI 

i|TJ 

ji« 

|||s 

.^<2  y 

«|1  ° 

|  e  § 

'S  §  ^ 

'^i^ 

Microhms. 

Ohms. 

Ohms. 

Ohms. 

Ohms. 

Silver  annealed 
,,      hard  drawn  . 

I-52I 

1-652 

0-01937 
O-O2IO3 

0-1544 

0-1680 

9!936 

•2214 
'241=; 

Copper  annealed    . 
,,      hard  drawn  . 

1-616 
1-652 

0-02057 
O-O2IO4 

0-1440 
0-1469 

9-718 
9-940 

T^      J 

•2064 
•2IO6 

Gold  annealed  .     . 
,,      hard  drawn  . 

2-081 
2-118 

0-02650 
0-02697 

0-4080 
0-4150 

12-52 
12-74 

•5849 

Aluminium  annealed 
Zinc  pressed      .     . 
Platinum  annealed  . 
Iron  annealed    .     . 
Nickel  annealed     . 
Tin  pressed  .     .     . 
Lead  pressed     .     . 

2-945 
5-689 
9-158 
9-825 

1  2  '60 
I3-36 

!9'85 

0-0375I 
0-07244 

0-1166 
0-1251 
0-1604 
0-1701 

0-2526 

0-0757 
0-4067 
1-96 

0-7654 
1-071 

0-9738 
2-257 

17-72 
34-22 

55-09 
59-10 

7578 
80-36 
1x9-39 

•1085 
•5831 

2-810 

1-097 

1-535 
1-396 
3*236 

Antimony  pressed  . 

35-90 

0-4571 

2-411 

216- 

Bismuth  pressed    . 
Mercury  liquid  .     . 

1327 
99-74 

1-689 
i  -2247 

13-03 
13-06 

798- 
578-6 

18-64 
18-72 

Platinum  silver  .     . 
Alloy  hard  or  anO 

24-66 

0-3140 

2-959 

I48-35 

nealed,    2   parts  I 

silver,  I  platinum  J 

German  silver  hard  1 
or  annealed        .  J 

21-17 

0-2695 

1-85 

127-32 

2-652 

Gold-silver    alloy  j 

hard  or  annealed,  1 

10-99 

0-1399 

1-668 

66-10 

2-391 

2  parts  gold,   i  | 

silver       .     .     .  ] 

25-2  Electricity  and  Magnetism.       [CHAP.  XVI. 

the  presence  of  other  metals  in  small  quantities.  Lead,  tin, 
zinc,  and  cadmium,  when  alloyed  with  one  another,  conduct 
electricity  as  if  the  component  parts  had  remained  separate 
and  were  arranged  as  a  bundle  of  conductors,  each  having 
a  uniform  section  throughout.  Alloys  of  bismuth,  antimony, 
platinum,  palladium,  iron,  aluminium,  gold,  copper,  silver, 
mercury,  and  probably  most  other  metals,  have  a  much 
greater  resistance  than  the  mean  resistance  of  their  com- 
ponent parts.  The  resistance  of  a  wire  one  metre  long, 
and  one  millimetre  in  diameter,  is  given  in  the  table  :  this  is 
equal  to  the  specific  resistance  multiplied  into  ^yffj  or 
12732.  The  resistances  of  the  wires  are  given  in  ohms, 
the  specific  resistances  in  microhms. 

Notes. — In  the  above  table  the  numbers  underlined  are  direct  obser- 
vations by  Dr.  Matthiessen,  B.  A.  Report,  1864. 

The  numbers  given  in  Col.  II.  (metre,  millimetre)  are  obtained  by 
calculating  the  value  in  Column  III.  for  lead  from  the  specific  gravity 
1 1 '376  (Table  II. ,  Electric  Conducting  Power  of  Alloys)  and  making 
the  other  numbers  in  the  column  inversely  proportional  to  the  conduct- 
ing powers  given  by  Dr.  Matthiessen,  when  hard  drawn  silver  is  100, 
and  gold  silver  alloy  15*03.  Column  III.  is  next  filled  in  by  calculating 
the  values  for  zinc,  platinum,  iron,  nickel,  tin,  antimony,  bismuth, 
mercury,  from  Column  II.  by  their  specific  gravities ;  the  three 
alloys  from  specific  gravities  given  by  Dr.  Matthiessen ;  the  silver, 
copper,  and  gold,  by  proportion,  from  the  hard  drawn  metals.  Except 
in  the  case  of  lead,  the  underlined  values  do  not  agree  with  Column  II., 
and  the  true  specific  gravity.  Column  IV.  is  calculated  from  Column 
II.  by  simply  multiplying  the  numbers  by  472-45  ;  and  Column  V. 
from  Column  III.  by  multiplying  the  numbers  by  I  '4337.  Column  I. 
is  calculated  from  Column  II.  by  dividing  the  numbers  in  Column  II. 
by  12,732. 

§  15.  The  specific  conductivity  of  a  material  is  the  re- 
ciprocal of  its  specific  resistance.  Thus  the  specific  conduc- 
tivity of  hard  silver  in  ohms  is  Tnnnnrrra*  =  6°53°°- 
There  is  a  common  but  most  reprehensible  practice  of 
referring  conductivities  to  some  material  such  as  silver. 
The  result  has  been  that  numerous  most  careful  experiments 
by  skilled  electricians  are  found  to  be  valueless,  for  no  two 


CHAP.  XVI.]      Measurement  of  Resistance.  253 

of  them  take  as  their  standard  metal  a  metal  with  the  same 
conductivity.  Nor  are  the  relative  conductivities  of  the 
standards  known.  Even  Dr.  Matthiessen's  experiments 
do  not  allow  the  construction  of  a  perfectly  satisfactory 
table. 

It  should  be  observed  that  while  copper  has  the  greatest 
conductivity  or  smallest  resistance  of  any  known  metal 
relatively  to  its  volume,  aluminium  has  the  smallest  resist- 
ance for  any  length  of  a  given  weight,  a  matter  frequently 
of  considerable  importance. 

§  16.  The  specific  resistance  of  all  metals  increases  as 
the  temperature  increases,  and  for  all  pure  metals  except 
iron  and  thallium,  Dr.  Matthiessen  found  that  the  rate  of 
increase  was  the  same.  The  resistance  R  of  a  metal  or 
alloy  at  the  temperature  ^expressed  in  degrees  Centigrade 
may  be  calculated  from  the  resistance  r  at  o°  Centigrade  by 
the  following  formula : 

R  =  r(l  +  at  ±  b?>)     .     .     .     11° 
The  following  are  the  values  of  a  and  b  : 

a  b 

Most  pure  metals   .         .         .     -003824  +  -00000126 

,,     Mercury        .         .         .     -0007485         -  -000000398 
,,     German  silver         .         .      -0004433          +   -000000152 
,,     Platinum  silver       .         .      -00031 
,,     Gold  silver    .         .         .     -0006999         —  •000000062 

According  to  experiments  by  Dr.  C.  W.  Siemens,  the 
resistance  r  for  any  temperature  up  to  one  thousand  degrees 
Centigrade  is  expressed  by  the  general  formula  r  =#  xi  + 
|8  T  +  y  (Bakerian  Lecture,  1871). 

Very  slight  impurities  increase  the  specific  resistance  of 
metals  considerably,  and  they  diminish  the  change  of 
specific  resistance  with  a  change  of  temperature. 

The  copper  wire  obtained  commercially  for  submarine 
cables  has  usually  a  specific  resistance  from  5  to  8  per  cent. 
higher  than  that  of  pure  soft  copper.  It  is  usually  tested  at 
24°  Centigrade,  at  which  temperature  the  resistance  of  a  foot 


254  Electricity  and  Magnetism.      [CHAP.  XVI. 

grain  of  pure  soft  copper  is  0*2262.  The  specified  resist- 
ance of  the  French  Atlantic  cable  at  that  temperature  was 
0-2456 ;  the  actual  mean  resistance  per  foot  grain  at  24° 
was  0-2388;  calling  R  the  resistance  per  knot,  w  the  weight 
in  Ibs.  per  knot,  and  s  the  resistance  per  foot  grain, 


W 

The  resistance  of  iron  used  in  telegraphy  is  given  by 
Latimer  Clark  as  7  times  that  of  pure  copper,  or  at  24° 
Centigrade  1-58  per  foot  grain:  different  specimens  vary 
considerably. 

§  17.  The  specific  resistance  of  insulating  materials  does  not 
admit  of  being  tabulated  in  the  same  manner  as  that  of  metals, 
because  slight  differences  in  the  preparation  of  the  materials 
cause  great  differences  of  specific  resistance,  and  because  of 
the  effects  of  electrification*  and  of  age.  Gutta-percha  and 
India-rubber  as  applied  to  insulate  submarine  cables  have 
been  the  subject  of  an  immense  series  of  careful  experiments. 
The  resistance  of  a  cubic  centimetre  of  gutta-percha,  a  fort- 
night old,  and  tested  at  24°  Centigrade  after  one  minute's 
electrification,  varies  from  about  25  x  io12  ohms  to  500  x 
io12  or  more.  The  mean  value  of  the  specific  resistance  of 
the  gutta-percha  employed  for  the  1865  Atlantic  cable  was 
342  x  jo12  (ohms)  after  one  minute's  electrification.  India- 
rubber  when  in  good  condition  has  a  still  higher  resistance. 
The  Persian  Gulf  cable  made  by  Hooper  had  a  specific 
resistance  of  about  7500  x  io12  ohms. 

Let  R  be  the  resistance  of  a  length  L  of  gutta-percha  cover- 
ing to  conduction,  from  the  wire  inside  to  the  water  outside, 
that  resistance  being  what  is  commonly  called  the  insula- 
tion resistance  of  the  covered  wire  or  core  of  a  submarine 
cable ;  let  M  be  the  specific  resistance  of  the  material  referred 

to  the  unit  of  volume ;  and  let  5  be  the  ratio  between  the 

a 
diameter  of  the  covering  and  that  of  the  covered  wire  :  then, 

*  The  effect  of  electrification  or  polarisation  in  causing  an  apparent 
increase  of  resistance  is  described  in  Chap.  IV.  §  io. 


CHAP.  XVI  ]      Measurement  of  Resistance.  255 

Ml°S?      ....    13° 
R  =  -3665  — — 

L  and  M  must  be  expressed  in  the  same  system  of  units. 
The  resistance  Rk  of  a  knot  of  cable  is 


M  log  - 


D 


14° 


506300 

where  M  is  the  specific  resistance  referred  as  above  to  centi- 
metres.     The  value  of — ^ —  adopted    by  M*r.  Latimer 
506300 

Clark  for  gutta-percha  at  75°  F  is  769,  corresponding  to  a  value 
for  M  equal  to  389  x  io6  megohms.  This  is  a  high  value. 
The  resistance  of  G.P.  increases  under  pressure.  Let  RP  be 
the  resistance  at  the  pressure  p  expressed  in  pounds  per 
square  inch,  and  R  the  resistance  at  the  atmospheric  pres- 
sure :  then,  approximately, 

RP  =  R  (i  +  0-00023 /.)     ...     15° 

The  constant  0*00023  probably  varies  for  different  speci- 
mens and  at  different  temperatures. 

The  resistance  of  G.  P.  also  increases  very  considerably  with 
age,  if  kept  under  Avater.  This  has  not  been  observed  with 
India-rubber.  The  resistance  of  some  specimens  of  India- 
rubber  tested  by  Dr.  Siemens  decreased  under  pressure. 

§  18.  We  may  calculate  the  resistance  of  an  insulating 
material  separating  two  conductors  in  the  following  way. 
Let  a  body  of  known  capacity  s  measured  in  microfarads  be 
charged  to  the  potential  P  measured  in  any  unit,  and  let  it 
be  gradually  discharged  through  a  great  resistance  R  such 
as  the  gutta-percha  covering  of  a  submarine  cable  offers  to 
conduction  through  the  insulating  envelope,  from  the  wire 
inside  to  water  outside — the  potential  of  the  water  being 
zero.  Let  the  potential  of  the  charged  conductor  fall  to  p 
in  the  time  /  measured  in  seconds ;  then  in  megohms 


°'4343 
slog^ 


256  Electricity  and  Magnetism.      [CHAP.  XVI. 

The  capacity  in  electrostatic  measure  of  covered  wire, 
neglecting  the  ends,  is  given  by  the  equation  6,  Chap.  V.;  to 
convert  this  into  electro-magnetic  measure,  we  must  divide 
the  value  by  v2  (§  2,  Chap.  VIII.)  ;  and  to  express  the  result 
in  microfarads  the  quotient  must  be  multiplied  by  io15  (Chap. 
X.  §  5)  :  hence  the  value  of  s  for  one  knot  or  6087  ft.  expressed 
in  microfarads  is 

4*2  x  6087  x  30*48  x  io15         _  0-2038 

4-6052  x  (28-8)2  x   io18  x  log1?-       log-  '    '  I7 

d  a 

Substituting  this  value  for  s  in  equation  (16),  we  have  for 
the  resistance  per  knot, 


R*  =  2'13'   log? 

This  formula  is  the  more  convenient  as  D,  d,  p,  p  may  be 
measured  in  any  units  as  the  ratios  only  are  required.  More- 

over, log  —  is  a  constant  for  any  one  cable.     The  values  of  P 
d 

and/  may  be  observed  on  any  electrometer,  or  by  means  of 
galvanometers,  using  the  method  described  in  the  chapter  on 
the  Measurement  of  Capacity. 

The  specific  resistance  of  very  short  specimens  of  wire  in- 
sulated by  different  materials  may  be  calculated  by  the  above 
method,  when  the  current  traversing  the  material  would  be 
insensible  even  on  the  most  sensitive  galvanometer. 

The  method  described  in  this  section  is  only  correct  if  R 
be  constant  throughout  the  experiment;  we  know  that  under 
electrification  it  actually  increases  from  minute  to  minute,  so 
that  the  result  given  by  the  formula  is  intermediate  between 
the  resistance  when  the  experiment  began  and  when  it 
ended. 

§  19.  A  rise  of  temperature  invariably  causes  a  decrease 
in  the  resistance  of  insulators.  Within  the  limits  of  o°  and 


CHAP.  XVI.]       Measurement  of  Resistance.  257 

24°  Centigrade  the  law  of  the  decrease  for  gutta-percha  is 
approximately  expressed  by  the  following  empirical  formula : 
Let  r.  be  the  resistance  of  the  material  at  the  higher 
temperature,  and  R  the  resistance  at  the  lower  temperature, 
and  let  /  be  the.  difference  of  temperature  in  degrees  Centi- 
grade :  then 

R  =  rator\og     -—  tlvga     .     .     .     19°; 

where  a  is  a  constant  varying  with  different  specimens  of 
gutta-percha  and  also  with  variations  in  the  time  of  electri- 
fication. The  value  of  log  a  increases  as  the  time  of  elec- 
trification increases,  and  is  also  higher  at  the  lower  tempera- 
tures. The  following  table  gives  values  of  log  a  for  different 
times  of  electrification  and  also  for  two  ranges  of  temperature, 
from  o°  to  12°  and  from  12°  to  24°,  derived  from  a  series  of 
experiments  made  on  a  knot  of  French  Atlantic  cable. 

Time  of  electrification  Between  o°  and  12°.  Between  12°  and  24°. 

in  minutes. 

1  -0562  -0532 

2  -06 1  'O544 

5  '0657  -0554 

10  -0686  -0560 

15  -0706  -057 

20  -0725  -0574 

25  -0729  -0578 

30  -0736  -058 

60  '0765  '0600 

'    90  or  more  '°747  -0618 

Thus  the  resistance  R,  after  one  minute's  electrification 
at  o°,  was  7,540  megohms.  Then,  to  find  the  resistance 
r  at  10°  after  the  same  time  of  electrification,  we  have 

log  .-  =1  10  x  0*0562  :  whence  r  =  '54°   _   20*0 
r  3*648 

The  following  is  a  table  of  the  relative  resistances  at  o°  and 
24°  after  various  times  of  electrification. 


258  Electricity  and  Magnetism.      [CHAP.  XVI. 

Minutes' electrification.         Resistance  at  o°.          Resistance  at  24' . 

1  7540  369 

2  9650  401 

5  12300  457 

10  14400  477 

20  17400  493 

30  18900  499 

60  21900  509 

90  24000  512 

It  should  be  observed  that  the  difference  in  resistance 
produced  by  electrification  is  much  greater  at  the  low  tem- 
peratures :  or,  putting  the  same  statement  in  another  form, 
there  is  a  much  greater  change  of  resistance  produced  by  a 
change  of  temperature  after  long  electrification  than  with 
short  electrification.  Experiments  have  been  most  frequently 
made  after  one  minute's  electrification. 

The  following  are  a  series  of  values  of  -  for  the  tempera- 
ture of  o°  and  24°  from  different  observations. 

•p 

Name  of  cable.  — .  Log  a. 

Persian  Gulf       .         .         .36-5  -0651 

Cores  in  which  thickness   of 

G.P.  does  not  exceed  -11 

in.  ...  23-62  '0572 

French  Atlantic 
Willoughby     Smith's      im 

proved  G.P.    . 


Silvertown  India-rubber 
Hooper's  India-rubber 


20-43  '°545 


28-14  -0604 

17-84 
3-01  -0199 


The  experiments  on  the  Silvertown  India-rubber  seem  to 
show  that  the  increase  of  resistance  does  not  follow  the  law 
expressed  by  equation  (19).  The  resistance  of  Hooper's 
material  on  the  contrary,  according  to  Mr.  Warren's  experi- 
ments, does  admit  of  being  calculated  by  that  formula  up  to 
the  temperature  of  38-33  Centigrade  :  the  resistance  is  halved 
by  a  further  increase  of  i8'33°. 


CHAP.  XVL]     Measurement  of  Resistance.  259 

The  electrification  of  Hooper's  material  is  still  more 
remarkable  than  that  of  gutta-percha  ;  with  one  specimen 
the  apparent  resistance  had  increased  fourfold  at  the  end  of 
10  minutes,  and  after  24  hours'  electrification  the  resistance 
was  23  times  greater  than  at  the  end  of  one  minute. 
According  to  Mr.  Warren,  if  Rt  is  the  resistance  after  one 

minute,  and  Rt  the  resistance  after  the  time  /,  the  ratio  —  is 

R/ 
constant  for  all  temperatures  with  this  material. 

§  20.  The  specific  resistance  of  other  insulating  materials 
than  India-rubber  and  gutta-percha  has  been  very  little  tested; 
that  of  glass  varies  immensely  in  different  specimens.  Ley- 
den  jars  may  be  found  which  do  not  lose  more  than  ^jth 
of  their  charge  per  diem,  and  the  greater  part  of  this  loss 
appears  to  be  due  to  conduction  over  the  surface,  or  creep- 
ing as  it  is  called,  rather  than  conduction  through  the  mass 
of  glass.  The  specific  resistance  of  some  kinds  of  glass 
is  therefore  nearly  infinite  ;  but  many  specimens  of  glass, 
especially  those  which  contain  lead,  hardly  insulate  as  well 
as  gutta-percha.  Vulcanite,  porcelain,  and  paraffin  are  good 
insulators,  but  I  am  aware  of  no  experiments  determining 
their  specific  resistance.  Liquid  paraffin  and  some  oils  are 
also  good  insulators. 

§  21.  Graphite  and  gas  coke  are  used  as  conductors  in 
batteries,  and  according  to  experiments  by  Matthiessen  their 
specific  resistance  referred  to  the  unit  of  volume  is  from 
about  1,450  to  40,000  times  that  of  pure  copper.  Tellurium 
and  red  phosphorus  have  still  higher  specific  resistances. 
The  following  table  gives  Dr.  Matthiessen's  results  expressed 
in  the  units  now  adopted. 


s  2 


260 


Electricity  and  Magnetism.       [CHAP.  XVI. 


Specific  Resistance  of  bad  Conductors,  computed  from  experiments  by  Dr. 
Alatthiessen. 


Materials. 

Resistance  in 
Microhms. 

Temperature 
Centigrade. 

•Graphite,  specimen  I 

2390 

22° 

„               2 

3780 

22° 

3 

41800 

22° 

Gas  coke  . 

4280 

25° 

Bunsen's  Battery,  coke 

67200 

26-2° 

Tellurium 

212500 

I9'6° 

ohms. 

.Red  Phosphorus         .         . 

132 

20° 

§  22.  The  specific  resistance  of  liquid  electrolytes  is  not 
very  accurately  known  owing  to  the  difficulty  in  measure- 
ment due  to  the  phenomenon  of  polarization.  A  rise  of 
temperature  diminishes  their  resistance  in  all  cases.  Its 
effect  has  been  studied  by  Becker  ('Ann.  d.  Chem.  u. 
Pharm.'  1850  and  1851)  and  by  Beetz  ('  Pogg.  Ann.'  cxvii. 
1862).  Paalzow  has  endeavoured  to  avoid  the  difficulty 
caused  by  polarization  by  using  composite  electrodes  con- 
sisting of  amalgamated  zinc  plates  in  porous  cells  containing 
solution  of  sulphate  of  zinc  ('Pogg.  Ann.'  cxxxvi.  1869). 
Kohlrausch  ('  Pogg.  Ann.'  cxxxviii.  1869)  has  used  the 
rapidly  alternating  -currents  of  a  magneto-electric  machine 
with  electrodes  of  very  large  surface.  J.  A.  Ewing  and  J.  G. 
MacGregor  ('Trans.  R.S.E.'  xxvii.  1873)  have  applied  the 
'bridge'  method  (§  11),  using  a  Thomson's  'dead  beat' 
mirror  galvanometer,  which  enabled  them  to  observe  the 
resistance  before  polarization  had  time  to  become  sensible. 

The  saturated  solution  is  frequently  not  the  best  con- 
ductor. This  is  the  case  with  sulphate  of  zinc  and  chloride 
of  sodium.  Sul'phuric  acid  when  diluted  with  water  has  a 
minimum  resistance  when  of  specific  gravity  1*25,  or  accord- 
ing to  other  experiments  when  45-84  grammes  of  SO3  are 
mixed  with  100  cubic  centimetres  of  water. 


CHAP.  XVI.]      Measurement  of  Resistance. 


261 


The  following  tables  show  the  resistance  of  some  of  the 
solutions  most  employed  in  batteries.     By  the  term  <  specific 
resistance  '  is  meant  the  resistance,  expressed  in  ohms,  of  one 
cubic  centimetre  to  conduction  between  opposed  faces. 
Sulphate,  of  Zinc  (at  IO°  Cent.}1 


Density. 

Specific 
Resist- 

Density. 

Specific 
Resist- 

Density. 

Specific 
Resistance. 

Density. 

Specific 
Resist- 

ance. 

ance. 

ance. 

I-OI40 

182-9 

•IOI9 

42T 

•2709 

28-5 

I-3530 

31-0 

I-OlS/ 

I40-5 

•1582 

337 

•2891 

28-3  min. 

I-4053 

32-I 

1-0278 

III'I 

•1845 

32-1 

•2895 

28-5 

I-4I74 

33*4 

I  -0540 
I  -0760 

638 
50-8 

•2186 
•2562 

30-3 
29-2 

•2987 
•3288 

-2S-7 
29-2 

I  -4220 
Saturated 

[33-7 

The  solution  of  maximum  conductivity  may  be  prepared 
by  dissolving  73*5  parts  of  salt  in  100  of  water. 

Sulphate  of  Copper  (at  10°  Cent.).1 


Density. 

Specific 
Resistance. 

Density. 

Specific 
Resistance. 

Density. 

Specific 
Resistance, 

1-0167 
I  -02l6 
1-0318 

I  -0622 

164-4 
134-8 
98-7 
59-0 

1-0858 
I-II74 
1-1386 
I-I432 

473 
38-I 

35-0 

34-i 

1-1679 
1-1823 
I-205I 
Saturated 

SI'? 
30^6 

}      29-3 

The  resistance  of  mixtures  of  these  salts  '  is  invariably  less 
than  the  mean  resistance  of  the  components,  being  in  many 
cases  less  than  that  of  either.' l 

Sulphuric  Acid— diluted? 


Specific 
gravity. 

0° 

4° 

8° 

12° 

16° 

20° 

24° 

28° 

Centigrade. 

TO 

'37 

I-I7 

I  '04 

•925 

•845 

786 

737 

•709     Resistance 

•20 

'S3 

I'll 

•926 

•792 

•666 

•567 

•486 

-411 

of  one  cubic 

•25 

•31 

1-09 

•896 

•743 

•624 

•S09 

•434 

•358 

centimetre  to 

•30 

•36 

I-I3 

•94 

•79 

•662 

•S6l 

•472 

•394 

conduction 

•40 

•69 

I-47|I-30 

1-16 

i  -os 

•964 

•896 

•839  ^ 

between  op- 

•50 

274 

2-4I  2T3 

1-89 

1-72 

1-61 

I-S2 

i-43 

posed   faces, 

I  '60 

4-82 

4-16  3-62 

vn 

2-7S 

2-46 

2-21 

2  -O2 

expressed  in 

170 

9-41  7-67  6-25  J5-I2 

4-23 

3-57 

3-07 

2-7I 

^ohms. 

1  Ewing  and  MacGregor. 


2  Becker. 


262  Electricity  and  Magnetism.      [CHAP.  XVII. 

Nitric  Add. 

2°        4°          8°        12°      1 6°        20°      24°      28°       •     Centigrade. 

)t  Resistance 
1-94  1-83  1-65   1-50  1-39     i -3  1-22  i-iSjof  one    cubic 
1  centimetre   in 
{     ohms. 

The  specific  resistance  of  water  (res.  of  cubic  centimetre)  when  pure  is 
9320  ohms,  computed  from  experiments  by  Pouillet.  The  presence  of 
smooth  of  sulphuric  acid  reduced  this  resistance  to  1550.  The  tempera- 
tures were  not  given  by  Pouillet. 

§  23.  When  the  resistance  of  'insulators  is  being  mea- 
sured, care  must  be  taken  to  prevent  conduction  over  the 
surface  of  the  insulating  material  between  the  two  conductors 
separated  by  that  insulator.  If,  for  instance,  a  conductor 
c,  Fig.  125,  supported  by  a  long  vulcanite  stem,  be  charged, 
and  the  gradual  fall  of  potential  tested  by  observing  the 
potential  on  an  electrometer,  the  insulation  resistance  of 
a  b  will  not  really  be  tested,  for  conduction  will  take  place 
almost  wholly  by  creeping  over  the  slightly  damp  or  dirty 
surface  from  a  to  b.  Similarly  the  insulation  resistance  of  a 
short  length  of  covered  wire,  Fig.  115,  will  be  very  incorrectly 
indicated  by  a  galvanometer  G,  unless  the  surface  of  the 
gutta-percha  near  A  separating  the  wire  from  the  water 
is  such  as  to  allow  no  creeping.  Surfaces  have  no  special 
conducting  power,  but  the  slight  film  of  damp  or  dirt 
conducts  in  proportion  to  its  sectional  area  and  the  con- 
ducting power  of  the  particular  kind  of  dirt.  Thus  brass 
filings  or  salt  with  a  little  moisture  form  a  highly  conducting 
film.  The  surface  of  glass  being  hygrometric  will  always  be 
covered  with  a  conducting  film,  unless  the  atmosphere  be 
artificially  dried  in  the  neighbourhood.  The  outer  layers  of 
gutta-percha,  soon  after  being  exposed  to  the  air,  become 
so  far  changed  as  to  insulate  badly,  so  that  the  surface 
should  always  be  fresh  cut  when  experiments '  are  being 
performed.  Old  vulcanite  is  often  found  covered  with  a 
conducting  film  resulting  from  the  decay  of  the  material. 
The  surface  of  old  glass  which  has  been  exposed  to  the 


FIG.  125. 


CHAP.  XVII.]  Capacities,  Potentials,  and  Quantities.    263 

weather  conducts  better  than  new  glass.  Mr.  Varley  gives 
the  following  recipe  for  preserving  and  renewing  the  insu- 
lating power  of  ebonite  or  vulcanite  supports  : — 

First,  wash  the  ebonite  with  water,  rubbing  it  well  till  dry ; 
secondly,  moisten  the  surface  of  the  ebonite  with  anhydrous 
paraffin  oil.  To  prepare  this,  put  a  quart  of  common 
paraffin  and  an  ounce  of  sodium  into  a  bottle. 

A  glass  support  or  the  inside  of  a  Leyden 
jar  is  best  cleansed  by  being  washed  with 
distilled  water  and  dried  at  a  fire  without 
being  wiped.  A  stem  such  as  a  b  may  then 
be  made  to  insulate  admirably  by  setting  it 
in  a  deep  narrow  tube  with  a  little  concen- 
trated sulphuric  acid  at  the  bottom.  To 
increase  the  resistance  of  the  conducting  film, 
its  sectional  area  must  be  diminished  as  much 
as  possible,  and  its  length  increased  :  hence 
a  long  rod  tf  b,  Fig.  125,  will  insulate  better 
than  a  short  one,  and  a  rod  of  small  surface 
better  than  oae  with  a  large  surface. 

The  resistance  of  a  film  of  dirt  does  not  appear  to  follow 
Ohm's  law.  When  the  potential  of  the  charged  and  insulated 
conductor  is  increased,  the  loss  by  creeping  increases  in  a 
much  higher  ratio  :  probably  the  conduction  is  partly  due  to 
numberless  small  discharges  from  one  speck  of  dirt  to  its 
neighbour. 


y  CHAPTER  XVII. 

COMPARISON   OF   CAPACITIES,  POTENTIALS,  AND    QUANTITIES. 

§  1.  THE  relative  throw  or  swing  of  a  galvanometer  needle 
caused  by  the  charging  or  discharging  of  two  conductors 
gives  a  very  convenient  method  of  comparing  their  capacities 
when  these  are  sufficiently  large.  Thus  let  x  y,  Fig.  126, 


264 


Electricity  and  Magnetism.      [CHAP.  XVII. 


represent  the  plates  of  a  condenser  separated  by  a  dielectric 
from  the  opposed  series  of  plates  a  b ;  let  a  b  be  connected 


with  the  earth,  and  let  x  y  be  connected  with  the  body  of  the 
key  M  ;  the  contacts  p  and  o  of  this  key  serve  at  will  to  con- 
nect #  y  with  the  zinc  pole  of  the  battery  z  c,  the  copper  pole 
of  which  is  to  earth,  and  with  the  one  terminal  of  the  galva- 
nometer G,  the  other  terminal  of  which  is  also  to  earth.  If 
the  handle  at  ivi  be  lifted,  the  condenser  x  y  will  be  charged 
with  negative  electricity.  On  depressing  M  this  charge  will 
flow  to  earth  through  the  galvanometer  G  ;  this  flow  will 
throw  the  needle  of  the  galvanometer  to  one  side  by  an 
impulse  of  very  short  duration.  If  the  needle  is  impeded  by 
no  friction,  calling  s  and  Sj  the  capacity  of  two  condensers, 
which,  when  charged  by  the  same  battery,  throw  the  needle 
to  the  angles  i  and  il9  we  have 


: :  sin  — 


sin 


The  current  is  proportional  to  the  capacities,  the  impulse 
is  proportional  to  the  current,  and  the  sines  of  half  the  angles 
are  proportional  to  the  impulses:  hence  we  have  the  above 
proportion.  Instead  of  observing  the  discharge  we  might  have 
placed  the  galvanometer  G  between  M  and  the  plates  x  y  of 


CHAP.  XVII.]  Capacities,  Potentials,  and  Quantities.    26$ 

the  condenser ;  in  that  case,  on  raising  M  we  should  observe 
the  throw  of  the  needle  produced  by  the  charge  when  flowing 
in  instead  of  when  flowing  out;  the  throw  in  the  two  cases 
is  the  same  if  there  is  no  leakage  from  x  y  to  a  b.  We 
might  substitute  for  the  earth  any  other  conductor,  joining 
E  EJ  and  E2  without  in  any  way  affecting  the  observation. 

§  2.  The  galvanometer  G  may  be  shunted  when  one  con- 
denser is  observed,  and  less  shunted  or  not  at  all  shunted 
when  a  second  condenser  is  tested ;  but  in  that  case  it  is 
necessary  to  take  care  that  the  resistance  of  the  shunts  bears 
the  same  relation  to  that  of  the  galvanometer  for  transient 
currents  as  for  permanent  currents.  The  self-induction  of 
the  shunt  and  the  galvanometer  may  be  very  different,  and 
may  seriously  affect  the  proportion  in  which  the  current  is 
subdivided  between  the  shunt  and  the  galvanometer. 

§  3.  A  differential  galvanometer  may  be  made  use  of  to 
compare  two  condensers,  the  capacities  of  which  are  nearly 
equal.  The  charges  given  to  the  two  condensers  by  the 
same  battery  must,  for  this  purpose,  be  passed  simul- 
taneously through  the  two  coils  of  the  galvanometer ;  the 
sine  of  half  the  throw  will  then  be  proportional  to  the  dif- 
ference between  them.  In  making  this  experiment  it  is  not 
necessary  that  the  coincidence  between  the  times  occupied 
by  the  passage  of  the  charges  should  be  absolute  ;  it  is 
sufficient  that  both  charges  pass  while  the  magnet  is  still 
sensibly  at  rest.  A  similar  comparison  may  be  made,  using 
a  simple  galvanometer,  by  the  following  device: — 

Pass  a  current  from  a  battery  c  z,  Fig.  127,  through  a  con- 
siderable resistance  R  R^  Connect  one  point  of  the  resistance 
R  R!  with  earth  at  E,  the  rest  of  the  system  being  insulated. 
Then  two  points  A  and  B  separated  from  E  by  equal  resistances 
will  be  at  equal  and  opposite  potentials.  Now  let  the  two 
condensers  to  be  compared  be  charged  respectively  by 
simultaneous  contact  with  A  and  B,  then  if  they  are  equal  they 
will  receive  opposite  and  equal  charges.  Next  connect  the 
two  condensers  one  with  another  (after  removing  both  from 


266 


Electricity  and  Magnetism.      [CHAP.  XVII. 


A  and  B)  ;  then  the  two  equal  charges  will  exactly  neutralize 
one  another,  and  no  charge  will  be  detected  in  either  con- 
denser. The  absence  or  presence  of  a  charge  may  be 
observed  by  galvanometer  or  electrometer.  The  proportion 

FIG.  127 


between  two  condensers  may  similarly  be  measured  by 
observing  the  proportion  between  the  resistances  A  E  and  E  B 
required  to  produce  charges  which  exactly  neutralize  one 
another.  The  capacities  will  be  inversely  proportional  to 
the  resistance  A  E  and  E  B.  These  resistances  must  be 
considerable,  or  the  potentials  at  A  and  B  will  be  insufficient 
to  charge  condensers  in  such  a  way  as  to  be  measured  by 
the  electrometer  or  galvanometer. 

The  points  A  and  B  may  be  connected  by  sliding  pieces 
to  successive  terminals  subdividing  R  R,. 
{      §  4.  For  small  capacities  Sir  William  Thomson's  platy- 
meter  and  sliding  condenser  may  be  used  (vide  Gibson  and 
Barclay,  spec.  Ind.,  cap.  Paraffin — Phil.  Trans.  1871). 

Let  there  be  two  equal  condensers/  and/1?  Fig.  128,  the 
outer  armatures  of  which  are  insulated  and  the  inner  armatures 
connected  with  an  electrometer.  Let  A  and  B  be  the  two 
condensers  which  are  to  be  compared ;  connect  the  outer 
armatures  of  A  and  B  with/ and /!  respectively,  and  their 
inner  armatures  with  the  earth. 

Let  A  be  so  constructed  that  its  capacity  can  be  varied  at 
will.  Charge  the  outer  armature  of  A  positively,  and  at  the 


CHAP,  xvii.]  Capacities,  Potentials,  and  Quantities.   267 

same  time  connect  the  point  q  with  the  earth ;  the  outer 
armature  of  p  will  take  a  positive  charge,  its  inner  armature 
a-  negative  charge;  p\  will  remain  uncharged.  Now  break 


FIG.  12 


contact  between  q  and  the  earth ;  the  electrometer  will  not 
deflect,  for  the  charge  in/  will  be  unaltered. 

Connect  the  outer  armatures  of  A  and  B  ;  if  the  ratio  of/ 
to  A  is  the  same  as  that  of  px  to  B,  the  potential  of  q  will 
remain  unchanged,  and  the  electrometer  will  not  be  de- 
flected; if  f.  is  greater  than  *-!  ,  the  potential  of  q  will  be 

A  15 

lowered ;  if  ^  is   less  than  t-|,  the  potential  of  q  will  be 

raised  by  the  connection  of  the  outer  armatures  of  A  and 
B.  The  deflections  of  the  electrometer  due  to  the  raising 
or  lowering  of  the  potential  of  q  allow  us  to  adjust  the 

capacity  of  A  until  the  ratio  <-  —  -O,    and   if  /  —  p\,  we 

shall  then  have  A  =  B.  A  can  therefore  be  adjusted  until 
it  is  exactly  equal  to  B. 

This  appears  to  be  the  best  method  for  copying  standard 
condensers,  because  it  does  not  depend  on  the  accuracy  of 
any  other  instrument.  Any  error  in  the  adjustment  of/  and 
pl  can  be  detected  and  allowed  for  by  reversing  the  position 


268  Electricity  and  Magnetism.      [CHAP  XVII. 

of  A  and  B.  The  relation  of  equality  is  not  required.  In 
order  that  no  deflection  be  produced  by  free  electricity  at  ^, 
it  is  sufficient  if 

/    :  A  =  A    :    B. 
The  analogy  with  the  Wheatstone's  bridge  is  obvious. 

§  5.  The  absolute  capacity  in  electrostatic  measure  of  any 
small  condenser  is  obtained  by  comparison  with  that  of  a 
sphere  of  known  dimensions  enclosed  within  another  sphere 
of  known  dimensions. 

The  absolute  capacity  of  larger   condensers  in  electro- 
magnetic measure  is  obtained  from  the  throw  i  of  the  needle 
of  a  galvanometer   through  which  an   instantaneous    dis- 
charge is  passed ;  we  have  the  capacity, 
t  sin  1  i 


S  =  2 

7T    Rj 

Where  /  is  half  the  period  or  time  of  a  complete  oscillation 
of  the  needle  of  the  galvanometer  when  no  current  is  pass- 
ing, and  R!  the  resistance  of  a  circuit  in  which  the  E.  M.  F. 
used  to  charge  the  condenser  would  produce  the  unit  de- 
flection ;  /  has  the  same  meaning  as  in  §  i.  In  a  reflecting 
galvanometer  half  the  deflection  may  be  taken  as  equal  to 
sin  \  i.  This  formula  follows  from  the  formula  for  the  im- 
pulse produced  by  the  current  on  the  magnet,  and  the 
formula  for  the  throw  produced  by  a  given  impulse.  In 
order  that  it  should  be  applicable,  the  impulse  must  be  very 
short  when  compared  with  the  time  /,  and  the  resistance  of 
the  air  must  be  insensible.  This  latter  condition  is  only 
fulfilled  when  successive  oscillations  of  the  needle  are 
sensibly  equal.  A  galvanometer  with  a  heavy  needle  should 
therefore  be  used  in  making  this  observation.  The  absolute 
value  of  the  difference  between  two  condensers  detected  by 
the  method  described  in  §  3  can  be  determined  in  this  way. 

§  6.  The  comparison  of  potentials  of  two  batteries  may 
be  made  indirectly  by  observing  the  currents  which  the  two 
batteries  are  capable  of  maintaining  through  known  resist- 


CHAP.  XVII.]  Capacities,  Potentials,  and  Quantities.    269 

ances ;  but  this  method  has  the  defect  that  the  electromo- 
tive force  of  most  batteries  varies  when  the  resistance  in 
circuit  is  changed,  being  higher  with  a  large  resistance  and 
lower  with  a  small  resistance  in  circuit.  The  potentials  can 
be  directly  compared  by  comparing  the  deflections  which  the 
two  batteries  produce  on  the  same  electrometer.  If  the 
difference  is  great,  a  graded  electrometer  must  be  em- 
ployed, or  the  following  method  may  be  used  :  charge  a. 
condenser  with  the  higher  potential ;  insulate  the  condenser, 
and  then  diminish  the  potential  in  a  known  and  convenient 
ratio  by  connecting  a  second  condenser  with  the  first,  the 
ratio  between  the  condensers  being  previously  determined. 
In  this  way  the  reduced  potential  may  be  brought  within 
the  range  of  the  electrometer  employed  to  measure  the 
lower  potential.  If  the  condenser  is  large,  the  electrometer 
may  be  dispensed  with  and  a  galvanometer  used  to 
indicate  the  relative  potentials,  to  which  the  condenser  is 
successively  charged  by  two  batteries.  The  two  discharges 
are  proportional  to  sin  \  i ;  and  as  the  capacity  of  the 
condenser  is  constant,  the  potentials  charging  the  con- 
densers are  proportional  to  sin  \  i,  or  in  the  case  of  mirror 
galvanometers  to  the  throw  of  the  spot  of  light ;  by  the  use 
of  shunts  on  the  galvanometer  this  method  is  extended  to 
the  comparison  of  potentials  differing  100  or  1000  fold. 

§  7.  A  quantity  of  electricity  is  seldom  measured  directly. 
A  known  current  flowing  for  a  given  time  conveys  a  de- 
finite quantity  of  electricity,  and  a  body  of  known  capacity 
charged  to  given  known  potential  also  contains  a  known 
quantity  of  electricity.  The  relative  quantities  per  unit  of 
surface  on  a  conductor  can  be  measured  by  the  proof  plane 
and  an  electrometer  as  already  described.  The  quantity  of 
electricity  producing  a  given  amount  of  heat  or  chemical  action 
is  best  measured  by  the  measurement  of  heat  or  of  the  weight 
of  material  electrolyzed.  The  quantity  Q  of  electricity  in  a 
very  short  current  flowing  through  a  galvanometer  is  given 
in  electromagnetic  measure  by  the  following  formula  : — 


2/O 


Electricity  and  Magnetism.    [CHA.P.  XVITI. 
Q  =  2  Cl-*  sin  1  /'..... 


2° 


Where  GJ  is  the  permanent  current  which  produces  the 
unit  deflection  on  the  galvanometer.  This  equation  follows 
from  equation  i. 


/  CHAPTER  XVIII. 

FRICTIONAL    ELECTRICAL    MACHINES. 

§  1.  THE  simplest  of  these  is  the  electrophorus,  which 
consists  of  two  parts  :  i.  a  disc  of  ebonite,  or  similar  material, 
A,  cemented  into  a  brass  disc  B,  uninsulated  ;  2.  a  brass  plate 
c  which  can  be  held  in  the  hand  by  an  insulating  stem  D. 
When  the  surface  of  the  ebonite  A  is  rubbed  with  flannel, 
silk,  or  a  catskin,  it  becomes  negatively  electrified  ;  if  the 
disc  c  be  now  superposed  on  the  electrified  disc  A,  and 
connected  with  the  earth  by  being  touched  with  the  finger, 
some  of  the  negative  electricity  on  A  is  conducted  to  earth. 
Some  of  the  negative  electricity  remains  on  A,  partly  because 
there  is  not  perfect  contact  all  over  the  surface  between  A 
and  c,  and  partly  because  the  electricity  on  A  is  not  wholly 
FIG.  129.  on  the  surface,  but  being 

attracted  by  the  disc  B,  has 
penetrated  the  mass  of  the 
vulcanite  in  the  manner 
indicated  by  the  electrifi- 
cation described  Chap.  V. 
§  6.  The  negative  electri- 
city remaining  on  and  in  A 
attracts  a  positive  charge 
to  the  lower  surface  of  c. 
If  the  finger  be  now  re- 
moved and  the  disc  c  lifted, 
it  retains  its  charge  of  positive  electricity,  which  may  be 


CHAP.  XV III. ]  Frictional  Electrical  Machines.  27 1 

seen  passing  to  earth  in  a  spark  if  the  knuckle  or  any  other 
blunt  conductor  is  brought  near  the  edge  of  c.  The  dis- 
charged disc  c  may  be  again  charged  by  being  placed  as 
before  on  the  disc  A  and  touched  by  the  finger,  and  this 
process  may  be  repeated  until  by  gradual  conduction  to  B 
and  c  the  original  charge  on  A  is  dissipated.  It  is  certain 
that  the  electricity  which  is  effective  in  inducing  a  charge  on 
c  does  not  lie  on  the  surface  of  A,  for  the  addition  of  one 
or  two  little  brass  pegs/j  passing  from  the  surface  of  A  to  B, 
improves  the  action  of  FIG 

the  electrophorus  :  this 
little  brass  peg  serves  to 
conduct  any  negative 
charge  which  may  accu- 
mulate on  the  surface  of 
A  to  the  earth.  The  elec- 
trophorus therefore  acts 
as  if  the  parts  were 
arranged  as  in  Fig.  130,  where  the  simple  vulcanite  disc 
A  is  replaced  by  a  metal  conducting  disc  a  a,  electrified 
with  negative  electricity,  and  separated  from  c  by  a  thin 
layer  of  dielectric,  and  from  B  by  a  thicker  layer  of  the  same 
dielectric. 

An  electrophorus  will  continue  to  give  sparks  in  rapid 
succession  for  a  considerable  period,  and  may  be  used  to 
charge  Leyden  jars.  A  cheap  electrophorus  may  be  made 
by  using  a  cake  of  resin  instead  of  vulcanite,  and  wooden 
discs  covered  with  tin  foil  instead  of  the  brass  pieces  B  and  c. 

§  2.  The  frictional  electrical  machine,  Fig.  131,  consists 
of  a  vulcanite  or  glass  disc  or  cylinder  A,  made  to  revolve 
between  cushions  or  rubbers  of  leather  or  silk  B  B,.  By  the 
friction  the  (silk)  rubbers  become  negatively,  and  the  glass 
positively  electrified.  The  difference  of  potential  depends 
on  the  substances  used  as  rubbers  and  disc ;  if  one  of 
these  be  put  to  earth,  the  other  will  be  raised  or  lowered  in 
potential  to  twice  the  extent  by  which  it  would  have  been 


2/2 


Electricity  and  Magnetism.    [CHAP.  XVIII. 


raised  or  lowered  if  both  were  insulated,  having  been  at 
the  potential  of  the  earth  before  commencing  the  experi- 
ment. This  action  is  precisely  analogous  to  that  which  occurs 

FIG.  131. 


r~ 


with  a  galvanic  cell ;  when  both  poles  are  insulated,  one  is 
raised  above  the  potential  of  the  earth,  and  the  other 
lowered  beneath  it.  Let  one  pole  be  put  to  earth,  the  po- 
tential of  the  other  is  immediately  doubled,  the  difference  of 
potentials  remaining  what  it  was  before.  Let  us  assume 
that  the  rubbers  in  an  electrical  machine  are  put  to  earth, 
then  the  positive  electricity  of  the  glass  is  collected  by  a 
series  of  points  D  D1?  placed  close  to  the  glass,  and  con- 
nected with  a  conductor  F  or  a  Leyden  jar.  The  glass  points 
are  sometimes  described  as  acting  by  induction  thus  :  the  + 
electricity  on  A  induces  —  electricity  on  the  points,  which 
springs  across  to  the  glass,  neutralizing  the  +  electricity  on 


CHAP.  XVIII.]    Frictional  Electrical  Machines.  273 

the  glass,  and  leaving  the  conductor  or  Leyden  jar  positively 
electrified.  There  is  neither  theoretical  nor  practical  differ- 
ence between  a  negative  spark  passing  from  D  to  A,  and 
a  positive  spark  passing  from  A  to  D,  and  we  may 
therefore  correctly  use  the  more  simple  statement  given 
above.  The  positive  electricity  which  the  glass  loses  is 
supplied  through  the  rubber  ;  a  stream  of  negative  elec- 
tricity flows  from  the  rubber  to  the  earth  while  the  con- 
ductor or  jar  is  being  charged;  and  this  is  only  saying  in 
other  words  that  positive  electricity  flows  from  the  earth  to 
the  rubber,  whence  it  crosses  to  the  glass  and  so  to  the 
conductor  F  or  to  a  Leyden  jar.  It  is  just  as  essential  to  the 
effective  working  of  the  electrical  machine  in  charging  a  jar 
that  the  outside  of  the  jar  be  to  earth,  as  that  the  rubber  be 
to  earth ;  and  if  the  outside  of  the  jar  and  the  rubber  be 
connected,  it  is  unnecessary  that  either  should  be  to  earth. 
It  is  necessary  in  order  to  charge  a  jar  or  conductor  as 
highly  as  the  machine  is  capable  of  doing,  that  the  electric 
circuit  should  be  complete,  except  across  the  dielectric  used 
to  insulate  the  conductor  to  be  charged.  It  is  of  no  import- 
ance whether  the  earth  form  part  of  that  circuit.  The 
parts  must  be  arranged  as  in  Fig.  132,  where  B  represents 
the  rubber,  A  the  rubbed  glass,  GGj  conducting  wires  or 
chains,  F  and  c  the  two  opposed  coatings  of  the  Leyden  jar 
and  D  the  dielectric ;  c  may  FlG>  ^2 

be  a  mere  brass  ball,  F  the 
walls  of  a  room,  and  D  the  air 
of  the  room.  The  case  will 
not  differ  from  that  of  an  ordi- 
nary Leyden  jar  except  as  to 
the  capacity  of  the  conductor 
c.  The  machine  B  A  will 
produce  the  full  difference  of 

potential  it  is  capable  of  producing  between  F  and  c.  The 
charge  given  to  c  will  simply  then  be  proportional  to  its 
capacity.  The  circuit  may  all  be  insulated;  it  may  be  put 


274  Electricity  and  Magnetism.    [CHAP.  XVIII. 

to  earth  between  B  and  F,  or  it  may  be  put  to  earth  between 
A  and  c.  The  only  effect  of  these  changes  will  be  to  alter 
the  absolute  potential  of  F  and  c,  but  not  to  alter  the 
difference.  If,  however,  G  and  Gl  are  both  put  to  earth,  the 
circuit  is  destroyed  and  no  effect  will  be  observed  at  F  or  c. 
Similarly,  if  G  or  G!  are  broken,  the  circuit  will  be  destroyed  ; 
but.  in  this  case  some  less  perfect  circuit  is  generally  com- 
pleted, which  will  lead  to  the  observation  of  some  electrical 
difference  between  F  and  c  if  either  G  or  G!  are  entire. 

§  3.  In  electrical  machines  sold  by  opticians,  large  brass 
conductors  F  F,  insulated  on  long  stems,  are  usually  con- 
nected with  the  collecting  points  D  D2  Fig.  131.  These  large 
conductors  have  a  sensible  capacity,  and  allow  the  machine 
to  produce  long  sparks  and  other  phenomena  requiring  the 
accumulation  of  a  considerable  quantity  of  electricity. 
The  addition  of  a  large  pasteboard  cylinder  with  rounded 
ends  covered  with  tin  foil  insulated  from  the  earth  by  a 
single  long  stem  and  connected  to  D  D,  by  a  wire  through 
the  air,  allows  the  volume  of  the  spark  obtained  from 
the  machine  to  be  greatly  increased.  The  insulating  stems 
are  best  made  of  vulcanite,  and  should  be  kept  clean, 
as  described  in  §  23,  Chapter  XVI.  No  points  or  sharp 
angles  must  form  part  of  the  system  of  conductors 
attached  to  DDI}  if  phenomena  requiring  great  differences 
of  potential  are  to  be  observed.  Glass  stems  and  discs  are 
old-fashioned.  They  are  weak,  hygroscopic,  and  when 
rubbed  with  hot  cloths  to  dry  them  become  covered  with 
fluff  which  conducts  the  electricity  to  earth. 

§  4.  The  friction  of  globules  of  pure  water  suspended  in 
steam  against  wood  and  other  insulators  may  be  made  use 
of  to  produce  electricity.  This  fact  was  discovered  by  Sir 
William  Armstrong,  whose  apparatus  was  made  as  fol- 
lows : — 

The  steam  issuing  from  a  high-pressure  boiler  by  the 
pipe  A  passes  in  a  series  of  tubes  (not  shown)  through  the 
box  B,  which  is  supplied  with  cold  water ;  from  these  tubes 


FIG.  133. 


CHAP.  XIX.]      Electrostatic  Inductive  Machines.        275 

the  steam  charged  with  condensed  globules  issues  through 
the  jets  c  c  c.  These  jets  are  lined  with  wood.  The  friction 
charges  the  steam  with 
positive  electricity,  which 
is  gathered  by  a  series  of 
points  at  D  attached  to'  the 
insulated  conductor  F.  The 
globules  of  water  must  be 
pure,  or  only  charged  with 
insulating  materials.  The 
resistance  of  pure  water  is 
so  great  that  it  may  be 
looked  upon  as  an  imperfect  insulator  of  the  same  class  as 
flannel ;  the  material  against  which  the  water  rubs  exercises, 
as  might  have  been  anticipated,  a  great  influence  on  the 
amount  and  sign  of  the  electricity  produced.  When  tur- 
pentine is  mixed  with  the  water,  the  vapour  becomes  nega- 
tively electrified. 


CHAPTER  XIX. 

ELECTROSTATIC   INDUCTIVE   MACHINES. 

§  1.  THE  action  of  the  electrophorus,  described  in  §  i, 
Chapter  XVIII.  may  be  imitated  by  arrangements  no  part  of 
which  requires  to  be  electrified  directly  by  friction;  and,  more- 
over, the  apparatus  can  be  arranged  so  that  the  inducing 
charge  shall  be  continually  strengthened  by  the  action  of 
the  machine.  Inductive  machines  of  this  kind  have  been 
invented  by  Bennett,  Nicholson,  Mr.  Varley,  Sir  William 
Thomson,  and  others.  Mechanical  energy  in  these  instru- 
ments is  converted  directly  into  an  accumulation  of  elec- 
tricity at  different  potentials,  the  work  done  being  expended 
in  overcoming  electrostatic  forces.  The  following  is  Mr. 
Yarley's  design: — 

T  2 


276  Electricity  and  Magnetism.       [CHAP.  XIX, 

A  series  of  metal  conductors,  c,  c,  c  (Fig.  134),  which  will 
be  called  carriers,  are  attached  by  means  of  a  vulcanite  disc  b 
to  the  axle  a,  which  can  be  made  to  rotate  at  pleasure.  The 


disc  and  carriers  rotate  between  two  pairs  of  metal  insulated 
cheeks,  ^and  e^  which  will  be  called  inductors.  The  knobs  // 
and  /Zj  are  in  connection  with  the  earth,  and  are  grazed  by 
the  carriers  c  c  as  they  revolve.  There  are  also  contact 
pins  at  g  and  g^  which  put  each  carrier  successively  in  con- 
tact with  e  and  with  *,  for  an  instant  in  passing. 

Let  a  small  charge  of  positive  electricity  be  communicated  to 
e,  the  rest  of  the  apparatus  being  at  the  potential  of  the  earth. 
The  plate  e  will  induce  a  negative  charge  in  c  as  it  rises 
past  /i,  the  positive  electricity  flowing  to  the  earth  through  h. 
The  carrier  c  conveys  this  negative  charge  to  ^j,  giving  up 
almost  the  whole  of  it  to  the  surrounding  inductor  plates  e{. 
This  redistribution  of  the  charge  leaves  c  almost  neutral, 
and  the  inductor  e\  next  induces  a  positive  charge  in  c  as 
it  descends  past  hi\  the  carrier  conveys  this  to  e  through 
the  pin  g,  and  so  augments  the  original  positive  charge. 


CHAP.  XIX.]      Electrostatic  Inductive  Machines.         277 

When  it  again  passes  h,  it  receives  by  induction  a  greater 
negative  charge  than  before,  which  again  augments  the 
negative  charge  in  *„  and  this  induces  a  new  positive  charge 
on  c,  which  is  transferred  to  e.  Each  turn  thus  augments  the 
charge  on  both  inductors  in  a  continually  increasing  ratio ; 
and  the  only  limit  to  the  charge  which  can  thus  be  accumu- 
lated on  the  inductors  is  that  determined  by  the  escape  of 
electricity  from  them  in  the  form  of  sparks  or  brushes.  A 
continuous  supply  of  sparks  may  be  drawn  from  e  or  e{.  The 
knobs  h  and  h\  need  not  be  in  connection  with  the  earth, 
provided  they  are  in  connection  with  one  another.  In  that 
case,  when  ^passes  h,  and^,  immediately  opposite,  passes  h^ 
c  and  ^!  are  connected  for  an  instant.  A  positive  charge  is 
induced  in  clt  and  a  negative  charge  in  c.  When  this  arrange- 
ment is  adopted,  one  of  the  inductors  may  be  in  connection 
with  the  earth. 

The  arrangement  adopted  by  Sir  William  Thomson  to 
replenish  Leyden  jars,  Chap.  XIV.  §  2,  in  which  he  wishes 
to  maintain  a  constant  potential,  is  very  compact.  The 
inductors  are  metal  plates  eel  bent  so  as  to  form  cylindrical 
surfaces,  as  in  Fig.  135.  The  axis  A  supports  two  carriers 
c  GU  which  are  also  parts  of  cylinders  not  exactly  concentric 
with  the  inductors.  In  the  fig.  the  axis  and  carriers  are  shown 
removed  from  their  positions  inside  the  inductors.  The 
connectors  are  shown  at  h  and  hlm  The  springs  ^and^j 
correspond  to  the  pins  with  the  same  letter  in  Mr.  Varley's 
arrangement.  In  the  mouse  mill,  another  arrangement  used 
by  Sir  William  Thomson  to  give  a  rapid  succession  of  sparks, 
the  inductors  are  parts  of  cylinders  and  the  carriers  are 
long  strips  like  the  staves  of  a  barrel.  The  smallest  con- 
ceivable charge  on  one  inductor  of  these  machines  is 
sufficient  to  start  them  •  indeed,  it  is  difficult,  if  not  impos- 
sible, so  completely  to  reduce  e  and  el  to  the  same  potential 
that  after  a  few  turns  of  the  carriers  they  shall  not  be  highly 
charged. 

§  2.  Holtz's  electrical  machine  is  an  inductive  machine  in 


278 


Electricity  and  Magnetism.       [CHAP.  XIX. 


which  the  carriers  are  replaced  by  the  imperfectly  conducting 
film  which  usually  covers  a  disc  of  glass,  or  by  the  external 
film  of  the  glass  itself  considered  as  a  body  capable  of 

FIG.  135. 


receiving  a  charge,  though  not  of  conducting  electricity. 
This  film  must  be  a  sufficiently  good  insulator  not  to  allow 
the  escape  of  the  charge  it  has  taken.  The  theory  of  the 
machine  will  be  more  readily  understood  if  we  replace  the 
imaginaiy  film  by  a  series  of  insulated  carriers  similar  to  those 
described  for  Mr.  Varley's  apparatus. 

Let  there  be  a  fixed  disc,  Fig.  136,  of  insulating  material 
B  and  a  rotating  disc  of  insulating  material  A  ;  on  each 
side  of  the  disc  A  let  there  be  a  series  of  metal  carriers  c 
and  d  all  insulated  from  one  another.  On  the  disc  B  let  there 
be  two  inductors  e  and  elt  the  first  positively  and  the 
second  negatively  charged,  e  and  el  'cover  both  sides  of 
disc  B  for  a  short  distance,  and  there  are  two  openings  F 
and  F,,  as  shown.  The  fixed  rods  h  and  h\  serve  to  join 
successive  pairs  of  carriers  d  and  d\  as  they  come  opposite 
e  and  ev  The  rods  h  and  /i}  are  shown  with  a  couple 
of  little  balls,  which  can  be  separated  to  show  sparks  pass- 


CHAP.  XIX.]      Electrostatic  Inductive  Machines.         279 

ing  along  the  connecting  rods  h  and  hv  There  are  also 
shown  two  springs  g  and  g\,  which  serve  to  connect  each 
carrier  c  in  succession  with  e  and  e{. 
Now  let  the  disc  A  revolve  so  that  the 
side  nearest  us  moves  in  the  direction  of 
the  arrow ;  when  c  is  opposite  e,  and 
c\  opposite  e},  d  and  d\  being  connected 
by  h  and  /zl5  there  will  be  a  positive 
charge  induced  on  the  external  surfaces 
of  d  and  <rl5  a  negative  charge  on  the 
external  surfaces  of  dl  and  c.  As  the  ro- 
tation continues,  each  of  these  carriers 
will  become  disconnected  from  h  and 
7z1?  and  will  carry  with  it  its  ^charge  of 
electricity  without  any  considerable 
change  in  the  distribution.  d±  and  cl 
will,  after  a  fraction  of  a  revolution, 
come  opposite  F,  where  they  are  shown 
as  ca.  and  da.  The  positively  charged 
carrier  ca  will  come  in  contact  with  the 
spring  g ;  at  the  same  time  c  and  d  will 
have  come  to  the  position  cb  and  db, 
and  the  negatively  charged  carrier  cb  will  come  in  contact  with 
the  spring  gv  There  will  then  be  a  redistribution  of  elec- 
tricity. The  capacity  of  ca  and  cb  is  diminished  by  the  absence 
of  the  plate  B  at  F  and  F1?  and  the  result  of  the  redistribution  is 
to  remove  the  greater  part  of  the  positive  electricity  from  ca  to 
e,  of  the  negative  electricity  from  cb  to  e^  to  set  free  negative 
electricity  on  da  and  positive  electricity  on  db.  When,  therefore, 
da  comes  under  h  into  the  position  of  d,  the  negative  elec- 
tricity flies  to  d\,  or,  in  other  words,  positive  electricity  flies 
from  d\  to  d,  and  the  cycle  of  operations  recommences.  The 
rods  h,  /215  the  carriers  c,  c^  &c.,  the  inductors  <?,  <?l5  and  the 
contact  springs  £•,  g^  all  play  exactly  the  same  part  in  Holtz's 
machine  as  in  Varley's,  with  the  exception  that  in  the  new 


280 


Electricity  and  Magnetism.       [CHAP.  XIX. 


FIG. 


arrangement  the  connectors  /i,  7i{,  instead  of  joining  c,  el 
directly,  join  a  new  set  of  carriers  d,  d^  &c.,  on  which  c,  cl 
induce  charges. 

The  actual  Holtz's  machine  has  no 
carrier.  There  is  a  fixed  disc  of  glass  B 
and  a  rotating  disc  of  glass  A.  At  the 
openings  F  and  Ft  there  are  the  in- 
ductors e  and  *,,  made  of  paper  ;  the 
connecting-pieces  £•  and  g\  are  also  of 
paper,  and  merely  point  at  the  place 
where  the  carriers  should  be  ;  the  con- 
nectors  //,  h±  are  brass  rods  ending  in 
5  1 1  points  opposite  c  and  rt;  the  part  of  the 

.  carriers  is  played  by  the  surface  of  the 
glass ;  the  action  is  identical  with  that 
described  for  carriers.  The  openings 
at  F!  and  F  serve  to  insulate  the  positive 
from  the  negative  parts  of  B  as  well  as 
to  alter  the  capacity  of  each  portion 
of  the  surface  of  A  as  it  passes  them  ; 
the  rods  h  and  /^  are  arranged  so  that 
they  can  be  withdrawn,  leaving  a  space 
at  n  across  which  sparks  pass ;  if  the 
space  be  gradually  increased  between  h 
and  /jj  at  nt  after  the  machine  has  been  set  in  action  by  charg- 
ing e  or  <?!,  a  splendid  violet  brush  of  some  inches  in  length 
may  be  observed  passing  at  n.  If  Leyden  jars  are  hung  on 
h  and  h\  to  increase  their  capacity,  this  brush  is  replaced 
by  a  torrent  of  brilliant  sparks.  With  large  Leyden  jars  on 
h  and  h^  one  spark  of  extraordinary  length  and  volume 
passes  at  sensible  intervals  of  perhaps  one  or  two  seconds. 

In  the  fig-ires  the  openings  F  and  F!  are  shown  as  if  they 
were  near  together,  because  the  whole  series  of  inductions 
can  thus  be  better  brought  into  one  view.  In  the  machine 
itself,  as  shown  in  Fig.  138,' the  openings  are  diametrically 
opposite  one  another,  and  the  electricity  is  collected  from 


1    + 


CHAP.  XX.]       Magneto-electrical  Apparatus. 


281 


the  glass  by  a  comb  or  series  of  points  H  and  H!  attached  to 
the  rods  h  and  hv  The  openings  F  and  FX  are  behind  the 
transparent  plate  A,  though  shown  in  the  full  lines. 

FIG.  138. 


The  dark  portions  of  the  figure  e  and  el  are  the  paper 
armatures  which  are  on  both  sides  of  B.  The  gear  is 
omitted  by  which  A  is  driven.  The  plate  B  is  carried  by  four 
supports  touching  its  edge. 


CHAPTER   XX. 

MAGNETO-ELECTRICAL   APPARATUS. 

§  1.  THE  phenomenon  described  in  Chapter  III.  §  §  18  and 
19,  and  more  fully  explained  in  Chapter  IX.,  is  often  de- 
scribed as  magneto-electric  induction  when  the  current  is 
induced  by  the  motion  of  a  wire  in  a  field  produced  by  a 
magnet,  the  term  electro-magnetic  induction-  being  reserved 
for  the  case  in  which  an  electric  current  induces  magnetism. 
The  1  distinction  in  this  sense  is  rather  popular  than  scientific, 

1  An  essential  and  scientific  distinction  can  be  drawn  between  the 
two  cases  by  applying  the  name,  magneto-electric  induction,  to  all  those 


282  Electricity  and  Magnetism.       [CHAP.  XX. 

but  it  is  convenient  to  retain  the  name  magneto-electrical 
apparatus  for  those  arrangements  in  which  powerful  electric 
currents  are  induced  in  wires  moved  across  a  magnetic  field 
produced  by  permanent  magnets  or  electro-magnets. 

In  magneto-electric  apparatus  the  moving  coils  of  wire 
must  be  driven  by  some  external  source  of  power. 

The  term  electro-magnetic  apparatus  is  used,  on  the 
contrary,  for  those  arrangements  in  which  the  battery  pro- 
ducing a  current  is  the  source  of  power  which  produces 
motion.  An  electro-magnetic  engine  is  one  which  may  be 
employed  to  drive  machinery. 

§  2.  Arrangements  giving  electrics-currents  by  the  relative 
motion  of  magnets  and  coils  were  invented  by  Pixii  and 
Ritchie.  The  apparatus  which  will  be  now  described  is 
generally  known  as  Clarke's  :  In  front  of  a  powerful  horse- 
shoe magnet  A,  Fig.  139,  there  are  two  bobbins  B  and  B!  of 
insulated  wire ;  these  two  bobbins  are  carried  by  one 
frame  v,  which  rotates  round  a  horizontal  axis,  being 
driven  by  a  pulley.  The  two  coils  of  wire  are  continuous, 
so  that  a  single  current  may  flow  round  both;  but  they 
are  so  joined  that  the  current  flows  in  a  right-handed  direc- 
tion round  one  and  flows  in  a  left-handed  direction  round 
the  other.  Each  bobbin  has  a  core  of  soft  iron,  and  these 
cores  are  joined  by  iron  at  the  back ;  that  is  to  say,  at 
the  ends  farthest  from  the  horse-shoe  magnet.  Two  ends  of 
the  wire  on  B  and  BL  are  directly  joined,  but  the  two  other 
ends  are  connected  through  a  set  of  springs  rubbing  on  suit- 
able contact  pieces  on  the  axis,  with  two  fixed  terminals  T  and 
TJ,  and  the  circuit  is  not  complete  till  these  are  joined.  We 
will  suppose  this  to  be  done.  As  the  coils  rotate,  each  soft 
iron  core  is  successively  magnetised  in  opposite  directions; 
thus  coil  B,  when  opposite  a  north  pole,  has  its  south  pole 
near  the  magnet  and  its  north  pole  at  the  back,  and  this 

cases  which  require  relative  motion,  and  using  electro-magnetic  induction 
to  denote  only  those  phenomena  of  induction  which  result  from  the 
change  of  currents  or  magnetism  without  relative  motion. 


CHAP.  XX.]       Magneto-electrical  Apparatus.  283 

arrangement  of  the  magnetism  is  reversed  when  B  is  opposite 
the  south  pole ;  thus  in  every  revolution  a  magnet  is,  as  it 
were,  introduced  into  B,  withdrawn,  and  replaced  with  its 
poles  in  the  opposite  direction,  and  again  withdrawn. 

FIG.  139. 


The  withdrawal  of  a  magnet  having  its  north  pole  at  one 
end  of  B,  and  the  introduction  of  a  magnet  having  its  south 
pole  at  the  same  end,  both  tend  to  induce  a  current  in  one 
direction  ;  but  the  withdrawal  of  this  second  magnet,  and  the 
introduction  of  the  reversed  magnet,  induce  a  current  in  the 
opposite  direction.  Thus  from  the  instant  the  coil  B  begins  to 
leave  the  pole  s,  to  that  instant  at  which  it  arrives  opposite 
N,  a  current  in  one  and  the  same  direction  is  being  induced; 
but  as  soon  as  B  begins  to  leave  N  and  return  to  s  the  direc- 
tion of  the  current  is  reversed,  and  continues  reversed  until 
opposite  s.  Thus  two  equal  and  opposite  currents  are 
induced  in  B  during  each  revolution.  The  same  statements 
hold  good  of  BJ,  but  when  the  current  induced  in  B  is  right- 


284  Electricity  and  Magnetism.        [CHAP.  XX. 

handed  that  in  B!  will  be  left-handed.  When  the  coils  are 
joined  as  described,  the  two  currents  are  added  to  one 
another ;  the  currents  can  be  observed  and  utilised  on  that 
portion  of  the  circuit  which  is  interposed  between  T  and  Tt. 
With  the  connections  as  described  the  currents  will  be 
reversed  between  T  and  T!  at  every  half-revolution  ;  but  it  is 
easy  to  arrange  a  set  of  contact  pieces  in  the  axis  so  that 
although  the  currents  must  necessarily  be  reversed  in  the 
coils,  they  flow  always  in  one  direction  between  T  and  TJ. 

§  3.  Even  when  flowing  in  one  direction  the  currents 
between  T  and  TI}  must  rise  to  a  maximum  and  decrease  to  a 
minimum  once  during  each  half-revolution. 
.  The  maximum  current  occurs  at  those  points  where  the 
armature  (as  the  soft  iron  continuous  core  may  be  termed) 
resists  the  motion  most  strongly.  At  these  points  the 
greatest  change  of  magnetism  is  taking  place  in  the  armature. 
The  motion  of  the  coils  alone  without  a  core  would  give 
rise  to  similar  but  much  weaker  currents.  The  best  length 
and  thickness  of  wire  depends  on  the  resistance  through 
which  the  current  is  required  to  flow  between  T  and  TJ. 
If  this  resistance  is  small,  the  coils  B  and  BJ  should  be  made 
of  thick  wire ;  if  the  external  resistance  is  great,  then  the 
coils  should  be  composed  of  many  turns  of  thin  wire. 

§  4.  Instead  of  a  simple  pair  of  bobbins  and  a  single 
horse-shoe  magnet,  we  may  arrange  any  convenient  number 
of  bobbins  on  a  ring  moving  in  front  of  the  poles  of  a  series 
of  magnets  also  arranged  in  a  circle.  Still  better,  we  may  let 
the  ring  of  coils  rotate  between  two  rings  of  magnets,  each 
coil  having  its  own  core,  which  is  alternately  magnetised  in 
opposite  directions  ;  each  coil  being  then  connected  with  its 
neighbour,  so  that  the  current  flows  alternately  in  a  right- 
handed  and  left-handed  direction,  we  add  the  electro-motive 
forces  due  to  all  the  coils. 

The  coils  may  be  joined  in  series,  or  the  pairs  may  be 
joined  in  multiple  arc,  the  former  plan  being  adopted  if 
the  object  is  to  get  a  great  E.  M.  F.  between  T  and  T!  ;  the 


CHAP.  XX.]       Magneto-electrical  Apparatus.  28,5 

latter  plan  if  our  object  is  to  obtain  a  moderate  E.  M.  F.}  with 
a  very  small  resistance  in  that  part  of  the  circuit  which 
forms  part  of  the  magneto-electric  machine.  Great  heat 
would  soon  be  developed  with  the  latter  plan.  With  the 
former  (coils  in  series)  very  perfect  insulation  is  required 
between  the  separate  layers  of  the  coils,  or  sparks  will 
perforate  the  insulating  substance  and  destroy  the  action 
of  the  coils.  The  following  is  a  description  of  a  machine  of 
this  class  constructed  by  Mr.  T.  Holmes,  and  successfully 
used  by  him  to  produce  the  current  for  a  large  electric 
lamp  : — 

The  coils,  eighty-eight  in  all,  are  fixed  in  the  rim  of  a 
wheel  about  five  feet  in  diameter,  with  their  axes  all  parallel 
to  the  axis  of  the  wheel.  They  are  arranged  in  two  rings,  each 
containing  forty-four  equally  spaced  bobbins.  The  centre 
of  each  bobbin  in  one  ring  corresponds  with  the  centre  of  the 
space  between  two  bobbins  in  the  other  ring.  This  wheel 
is  driven  at  about  no  revolutions  per  minute.  Horse-shoe 
magnets  are  fixed  in  a  frame  round  the  circumference  of  the 
wheel  in  three  planes,  or  rings,  containing  twenty-two  each. 
The  two  poles  of  each  magnet  are  in  the  same  plane,  or  ring. 
The  distance  between  their  poles  is  equal  to  the  distance 
between  the  bobbins,  or  coils.  The  magnets  in  the  two 
outside  rings  have  similar  poles  opposite  one  another.  The 
magnets  in  the  inner  ring  are  placed  with  opposite  poles 
facing  the  two  similar  poles  of  the  outer  rings.  The  two  out- 
side rings  have  compound  magnets  of  four  steel  plates  ;  the 
magnets  of  the  inner  ring  between  the  two  sets  of  bobbins 
have  t  six  plates.  The  weight  of  each  plate  is  six  pounds. 
Alternate  coils  have  their  iron  cores  magnetised  in  oppo- 
site directions,  but  the  wires  are  so  connected  in  series  that 
the  induced  currents  flow  all  in  the  same  direction  relatively 
to  the  wire.  The  length  of  the  hollow  iron  core  inside  each 
bobbin  is  3^  inches.  Its  external  diameter,  i^  inch ;  its 
internal  diameter,  i  inch.  Two  copper  wires,  "148  inch  in 
diameter,  forty-five  feet  long,  are  wound  round  each  core 


286  Electricity  and  Magnetism.        [CHAP.  XX. 

and  connected  in  double  arc.  These  wires  are  equivalent  to 
one  wire  '2  inch  in  diameter  of  the  same  length.  The  iron 
core  and  brass  bobbin  surrounding  it  are  split ;  that  is  to  say, 
an  open  slit  is  left  down  one  side  of  each  cylinder.  This 
prevents  the  induction  of  currents  in  the  bobbin  and  wire 
where  they  are  not  wanted. 

Each  ring  induces  forty-four  distinct  currents  during  one 
revolution  of  the  wheel,  and  the  maximum  current  from  one 
ring  coincides  with  the  minimum  current  from  the  other  ;  and 
as  each  current  lasts  a  very  sensible  time,  and  by  a  commuta- 
tor is  transmitted  always  in  one  direction,  their  combination 
does  not  produce  a  series  of  sparks,  but  a  nearly  constant  and 
uniform  current.  One  and  a  quarter  horse-power  is  re- 
quired to  drive  the  machine  when  in  action,  and  much  less 
when  the  circuit  is  broken  so  as  to  stop  the  induced  current. 
This  machine  offers  a  striking  example  of  the  transformation 
of  work  into  a  current  of  electricity. 

§  5.  If  the  change  of  magnetisation  could  take  place  in- 
stantaneously, there  would  be  no  limit  to  the  electromotive 
force  which  these  machines  could  produce,  except  the  limit 
imposed  by  the  difficulty  of  insulating  the  wire  and  of  driving 
the  coils  against  a  great  mechanical  resistance ;  the  electro- 
motive force  induced  in  the  coils  would  increase  in  direct  pro- 
portion to  the  speed  at  which  they  were  driven.  Practically 
owing  to  the  coercive  force  of  even  the  softest  iron  and  the 
self-induction  of  the  wire  on  the  bobbins,  the  change  of 
magnetisation  and  of  direction  of  the  current  occupies  a  very 
sensible  time,  and  if  the  speed  be  increased  beyond  that  at 
which  the  greatest  change  of  magnetisation  occurs,  the  elec- 
tromotive force  will  fall  off  instead  of  increasing.  The  effect 
of  the  coercive  force  is  diminished  as  stated  above  by  making 
the  core  hollow,  and  the  effect  of  useless  induction  is  dimin- 
ished by  splitting  it  from  end  to  end. 

§  6.  Obviously  the  magnets  used  to  induce  the  currents 
might  be  electro-magnets  ;  but  if  these  were  excited  by  an 
independent  battery,  the  induced  current  would  be  obtained 


CHAP.  XX.]         Magneto-electrical  Apparatus.  287 

at  a  much  greater  cost  than  would  give  the  same  current 
directly  from  a  battery. 

Mr.  Wilde  conceived  the  happy  idea  of  using  a  current  in- 
duced by  permanent  magnets  to  excite  a  large  electro-magnet 
which  is  used  to  induce  a  second  current,  which  can  be  so 
much  greater  than  the  first  as  the  electro-magnet  is  more 
powerful  than  the  permanent  magnet.  The  second  current 
may  be  used  to  excite  a  second  electro-magnet  still  more 
powerful  than  the  first,  and  this  second  electro-magnet  used 
to  induce  a  third  current  greater  than  either  of  the  two 
others.  Dr.  Siemens  and  Professor  Wheatstone  simultane- 
ously invented  a  further  extension  of  the  same  idea.  They  use 
the  current  induced  by  the  permanent  magnet  to  convert 
this  magnet  itself  into  an  electro-magnet.  The  effect  is  very 
remarkable.  However  weak  the  permanent  magnetism  in 
the  inducing  magnet  may  be  in  the  first  instance,  a  few  rapid 
turns  of  the  coils  with  their  armatures  induces  a  current 
which  increases  in  geometrical  proportion,  increasing  the 
magnetism  of  the  inducing  magnet  at  the  same  time,  until 
the  resistance  of  the  armatures  as  they  pass  the  poles  is 
such  as  to  balance  the  driving  power.  The  current  in 
the  main  circuit  may  be  directly  utilised,  or  one  portion 
of  it  may  be  shunted  for  use  while  the  other  branch 
maintains  the  magnetism  of  the  electro-magnet.  Mr.  Ladd 
modifies  this  arrangement  by  having  two  distinct  coils  on 
his  armature,  one  of  which  is  used  to  excite  the  electro- 
magnet, while  the  other  conveys  the  induced  current  which 
is  to  be  utilised  outside  the  machine.  Ladd's,  Wilde's,  and 
Siemens'  machines  will  produce  currents  capable  effusing  an 
iron  rod  an  inch  in  diameter  and  a  foot  long.  The  arma- 
tures and  coils  become  themselves  so  hot  that  they  must 
be  artificially  cooled,  or  the  machine  can  only  be  worked  for 
short  periods  without  being  permanently  injured. 

§  7.  The  armature  used  in  these  new  machines  is  generally 
of  the  form  introduced  by  Messrs.  Siemens,  which  is  much 
superior  to  that  in  Clarke's  apparatus. 


288 


Electricity  and  Magnetism.        [CHAP.  XX. 


The  compound  horse-shoe  magnets  are  arranged  in  a  pile 
of  considerable  depth,  each  separated  from  its  neighbour  by 
a  sensible  space,  as  shown  in  Fig.  140.  The  armature  A  A, 
rotates  round  the  axis  x  Y  between  the  poles  in  a  position 
where  the  magnetic  field  is  much  more  intense  than  that 

FIG.  140. 
Sectional  Elevation. 

Plan. 

A 


occupied  by  Clarke's  armature.  This  armature  is  a  long  bar 
of  soft  iron  of  an  frH  section,  as  shown  in  plan  at  A  (Fig.  140), 
and  is  magnetised  transversely.  The  wire  is  wound  round  it 
longitudinally,  passing  up  one  side  and  down  the  other. 

As  this  armature  rotates  round  the  axis  x  Y  its  magnetism 
is  reversed,  and  at  each  reversal  a  current  is  induced  in  the 
enveloping  wire.  The  intensity  and  uniformity  of  the  mag- 
netic field  in  which  the  wire  is  placed  cause  this  arrangement 
to  give  much  better  results  than  those  obtained  by  Clarke's 
arrangement. 

§  8.  It  is  unnecessary  that  the  armature  either  of  Siemens' 
or  Clarke's  or  any  magneto-electric  machine  should  com- 
plete one  or  more  revolutions  in  order  to  induce  a  current : 


CHAP.  XX.]       Magneto-electrical  Apparatus.  289 

the  smallest  motion  about  the  axis  is  sufficient  to  produce 
some  electromotive  force,  because  it  will  change  the  intensity 
of  the  field  in  which  the  armature  is  placed.  With  Siemens' 
armature  especially  a  very  small  deviation  in  one  direction 
from  the  position  shown  in  the  plan,  Fig.  140,  will  give  a 
powerful  current.  The  wires  of  the  coil  move  almost  directly 
across  the  lines  of  magnetic  force,  and  the  armature  will  be 
so  magnetised  as  to  help  the  induction  so  produced.  A  slight 
motion  in  one  direction  will  induce  a  positive  current,  a 
slight  motion  in  the  opposite  direction  a  negative  current. 
Keys  for  sending  electric  signals  without  batteries  are  con- 
structed on  this  principle. 

§  9.  The  Inductorium,  or  Ruhmkorjfs  coil,  is  strictly 
speaking  an  electro-magnetic  apparatus,  inasmuch  as  the 
inducing  magnet  is  not  moved,  but  is  magnetised  and  de-mag- 
netised by  the  passage  and  interruption  of  a  current  from  a 
battery.  It  is  used  to  obtain  by  induction  a  great  electro- 
motive force  from  a  battery  of  small  electromotive  force.  The 
inductorium  consists  of  an  electro-magnet  excited  by  a  com- 
paratively short  coil  of  thick  wire  called  the  primary  coil  :  a 
long  coil  of  fine  wire,  called  the  secondary  coil,  is  wound 
round  the  same  electro-magnet ;  the  primary  circuit,  which 
is  completed  by  a  battery  of  small  resistance  such  as  Grove's, 
is  alternately  made  and  broken  with  great  rapidity ;  the 
secondary  circuit  is  always  complete,  or  interrupted  only  by 
such  a  space  that  the  electromotive  force  induced  in  the 
secondary  is  sufficient  to  cause  the  passage  of  a  spark 
WThen  the  primary  circuit  is  closed,  the  electro-magnetism  of 
the  core  induces  a  current  in  the  secondary  wire  in  a  direc- 
tion opposed  to  that  of  the  primary  circuit.  When  the 
primary  circuit  is  interrupted,  the  diminution  of  the  mag- 
netism in  the  core  induces  a  current  in  the  same  direction 
round  the  wire  as  the  primary  current,  and  therefore  in  a 
direction  through  the  secondary  coil  opposed  to  the  current 
previously  induced. 

The   electromotive   force   per    foot   of  the   wire   in  the 


2  go 


Electricity  and  Magnetism.        [CHAP.  XX. 


secondary  coil  depends  on  the  intensity  of  the  magnetic 
field  produced  and  on  the  rapidity  with  which  it  is  produced. 
The  sum  of  the  electromotive  forces  thus  induced  in  a  long 
coil  is  enormously  greater  than  the  E.  M.  F.  of  the  inducing 
battery ;  the  longer  the  secondary  coil  the  greater  the 
electromotive  force. 

§  10.  Sparks  many  inches  in  length  can  be  obtained  from 
the  secondary  'circuit  of  a  large  inductorium,  but  in  such 
apparatus  the  greatest  care  is  requisite  in  the  insulation  of 
the  secondary  coil.  Each  wire  must  be  insulated  from  its 
neighbour  by  layers  of  some  hard  insulator  which  a  spark  will 
not  easily  pierce,  and  care  must  be  taken  so  to  wind  the  coil 
that  no  two  portions  of  the  secondary  coil  at  very  different 
potentials  are  near  together :  this  is  effected  by  winding  the 
coil  in  successive  compartments  A,  B,  c,  as  in  Fig.  141,  where 
each  compartment  is  insulated  from  its  neighbour  by  discs 

FIG.  141. 


of  vulcanite.  In  order  to  facilitate  the  rapid  change  of  mag- 
netism, the  core  should  be  either  a  hollow  split  cylinder  or  a 
bundle  of  iron  rods  insulated  from  one  another. 

The  making  and  breaking  of  the  primary  current  is  gene- 
rally effected  by  a  little  oscillating  hammer  having  a  small 
armature  of  soft  iron  at  its  head  :  this  hammer  is  placed  so 
as  to  be  attracted  when  the  iron  core  is  magnetised  ;  by  its 
motion  towards  the  core  it  breaks  the  primary  circuit ;  the 
core  being  no  longer  magnetised  allows  the  little  hammer  to 
fall  back  and  so  once  more  to  complete  the  primary  circuit ; 
this  re-magnetises  the  core,  and  the  hammer  again  breaks  the 
circuit,  and  this  action  repeats  itself  indefinitely.  There  are 


CHAP.  XX.]       Magneto-electrical  Apparatus.  291 

adjustments  by  which  the  rapidity  of  the  oscillations  of  the 
hammer  can  be  regulated  until  the  best  result  is  obtained. 
The  limit  to  the  speed  at  which  the  successive  currents  can 
be  induced  depends  on  the  coercive  force  of  the  iron  core 
and  the  self-induction  of  the  secondary  coil.  The  work 
done  in  the  secondary  coil  by  the  induced  current  is  neces- 
sarily less  than  that  done  in  the  primary  coil  by  the  battery, 
however  much  greater  the  electromotive  force  may  be. 

The  following  is  a  description  of  an  inductorium  made  by 
Messrs.  Siemens  : — The  core  is  made  of  iron  wires  1*3  m.m. 
diameter  and  95  centimetres  long.  These  are  cemented  to- 
gether and  form  a  cylinder  60  m.m.  diameter.  Two  layers  of 
copper  wire  2*5  m.m.  diameter  form  the  primary  coil.  This 
coil  and  the  iron  core  weigh  35  Ibs.  They  are  placed  in  a 
tube  of  hard  vulcanite  26  m.m.  thick  at  the  ends,  and  12 
m.m.  thick  at  the  middle  :  along  this  tube  150  thin  discs  of 
vulcanite  are  fixed  at  equal  intervals,  and  the  ends  are 
covered  with  thick  discs  of  the  same  material.  Each  sub- 
division between  the  little  discs  is  filled  with  a  coil  of  fine 
silk-covered  and  varnished  copper  wire  0-14  m.m.  diameter  : 
these  coils  are  connected  in  series,  so  that  the  current  flows 
from  the  outside  to  the  inside  of  one  compartment  and  from 
the  inside  to  the  oatside  of  the  next,  in  order  that  no  two 
portions  of  wire  at  greatly  differing  potentials  may  ever  be 
in  close  proximity.  The  length  of  the  secondary  coil  is 
10,755  metres,  and  it  makes  299,198  -turns  round  the 
cylinder.  The  weight  of  the  copper  wire  is  58  Ibs.  and  its 
resistance  about  155,000  ohms. 

There  is  some  difficulty  in  arranging  a  good  make  and 
break  piece  acted  upon  by  the  hammer  on  account  of  the 
large  sparks  which  pass  between  the  contacts  tending  to 
fuse  them  together  and  oxidise  them.  Messrs.  Siemens 
make  contact  between  a  platinum  point  and  a  platinum  or 
silver  amalgam  covered  with  alcohol. 

When  long  sparks  are  wanted,  the  make  and  break  appa- 
ratus is  driven  slowly,  by  clockwork  or  by  a  separate 

U  2 


292  Electricity  and  Magnetism.        [CHAP.  XX. 

electro-magnetic  engine,  so  as  to  give  a  long  contact,  which 
is  then  suddenly  broken.  The  above  apparatus  will  give 
sparks  of  from  one  to  two  feet  in  length,  with  six  large 
Grove's  elements  in  the  primary  circuit :  50  miles  of  fine 
wire  have  been  used  in  some  induction  coils. 

§  11.  A  Leyden  jar  or  some  other  form  of  condenser  is 
frequently  attached  to  the  secondary  circuit  when  this  is 
used  to  give  sparks.  The  one  armature  of  the  condenser  is 
connected  with  one  end  of  the  secondary  wire  and  the 
other  armature  with  the  other  end  of  the  same  wire,  near  the 
oppcsed  points  across  which  the  spark  is  to  pass ;  the  effect 
of  this  arrangement  is  that  a  considerable  accumulation  of 
electricity  takes  place  near  the  points  before  the  difference 
of  potential  is  sufficient  to  cause  the  spark  to  pass,  and  con- 
sequently the  number  of  sparks  observed  in  a  given  time  is 
less  with  the  condenser  than  without,  but  each  spark  con- 
veys more  electricity  and  is  much  more  brilliant.  An  electro- 
motive force  in  the  coil  insufficient  to  cause  any  spark  to 
pass  may  nevertheless  help  to  charge  the  armatures  of  the 
condenser,  and  thus  some  portions  of  the  inductive  action 
may  be  utilised  with  the  condenser  which  without  it  would 
be  wasted.  The  dielectric  must  be  thick  and  strong,  or  it 
will  be  pierced  by  the  spark. 

A  condenser  is  also  frequently  employed,  connected  with 
the  primary  circuit. 

§  12.  The  Inductorium  may  be  used  to  give  the  sparks 
required  for  examination  by  the  spectroscope  or  to  give  an 
electric  light,  which  is,  however,  comparatively  feeble.  It  may 
be  used  to  charge  Leyden  jars  and  produce  physiological 
effects ;  it  may  be  used  to  produce  the  beautiful  luminous 
effects  which  occur  when  electricity  is  passed  through 
rarefied  gases.  The  gases  are  enclosed  in  glass  tubes  having 
platinum  electrodes  soldered  into  the  glass  and  terminating 
in  balls  at  a  considerable  distance  apart :  instead  of  the 
spark  observed  in  air,  a  diffused  light  is  seen  differently 
coloured  in  various  gases  and  beautifully  stratified.  These 


CHAP.  XXI.]        Electro-magnetic  Engines.  293 

appearances  have  been  carefully  studied  by  Gassiot,  Pliicker, 
and  others.  The  tubes  enclosing  the  gases  may  be  bent 
into  very  complicated  shapes,  and  filled  in  different  parts 
with  different  gases,  so  as  to  produce  a  striking  and  pretty 
appearance  when  the  current  from  the  inductorium  passes  : 
they  are  generally  called  Geissler  tubes.  The  induction  of  a 
magnet,  or  of  a  current  of  electricity,  or  of  a  simple  conductor 
outside  the  tubes,  can  be  observed  on  the  luminous  current 
within,  causing  it  to  be  distorted  or  move  in  those  directions 
in  which  the  inductive  force  would  act  on  a  solid  wire  con- 
ducting a  similar  current :  for  this  experiment  the  tube  must 
be  wide  or  nearly  spherical,  so  that  the  luminous  current 
occupies  only  a  portion  of  the  enclosed  space. 


CHAPTER   XXI. 

ELECTRO-MAGNETIC    ENGINES. 

§  1.  THE  most  elementary  arrangements  by  which  electricity 
can  be  made  to  produce  regular  motion  by  electro-magnetic 
force  are  those  in  which  a  short  wire  or  rod  conveying  a 
current  is  made  to  rotate  by  the  direct  and  continuous 
electro-magnetic  attraction  to  or  repulsion  from  some  fixed 
conductor  conveying  the  same  or  another  current. 

Let  o  P,  Fig.  142,  be  a  wire  capable  of  rotation  round  o, 

Frc.   742.  FIG.  143. 


and  conveying  a  current  from  the  centre  to  the  circumference 
of  a    ring-shaped  trough  of  mercury  into   which   the  end 


294  Electricity  and  Magnetism.        [CHAP.  XXI. 

of  the  wire  P  dips.  Let  the  same  current  or  another  be 
conveyed  in  a  straight  wire  A  B  near  the  edge  of  the 
mercury  ring.  Then  the  wire  o  P  will  be  attracted  by 
A  B  until  P  reaches  the  position  PJ,  Chap  III.  §  6 ;  the  wire 
will  then  be  repelled  till  it- reaches  the  position  pm,when  it 
will  be  again  attracted,  and  thus  continuous  rotation  rnay 
be  produced  in  the  direction  shown  by  the  arrow,  if  the 
other  portions  of  the  circuit  are  arranged  so  as  not  to  neu- 
tralise the  series  of  actions  described.  The  force  available 
even  with  very  powerful  currents  is  small. 

Again,  let  the  fixed  current  flow  in  the  circle  A  B  as  shown 
by  the  arrow,  Fig.  143 ;  the  moveable  wire  o  P  in  which  a 
current  flows  from  the  centre  to  the  circumference  will  be  con- 
tinuously impelled  to  rotate  in  a  direction  -opposed  to  that  of 
the  fixed  current.  The  force  will  be  very  small,  but  we  may 
multiply  it  by  using  a  coil  of  many  turns  for  the  conductor 
A  B.  No  convenient  way  has  yet  been  found  of  multiply- 
ing the  conductor,  o  P,  and  the  power  given  out  by  this 
arrangement  is  therefore  still  very  small. 

A  horizontal  circular  current  also  tends  to  produce  con- 
tinuous rotation  in  a  vertical  current  approaching  it  or  receding 
from  it.  Thus  let  a  moveable  system  P  M  P,,  Fig.  144,  be 

FIG.  144. 


placed  in  the  centre  of  a  fixed  ring  A  B,  through  which  a 
current  flows  as  shown  by  the  arrow.  Let  the  ends  P  and 
p,  dip  in  a  mercury  trough,  by  which  the  circuit  through 


CHAP.  XXL]        Electro-*,  \:ignetic  Engines. 


295 


o  P  and  o  PL  may  be  maintained  :  both  vertical  currents  de- 
scending to  P  and  P!  are  acted  upon  in  one  direction  by  the 
fixed  current,  and  tend  to  turn  P  M  PJ  in  a  direction  opposed 
to  that  of  the  current  in  A  B. 

§  2.  Currents  can  be  made  to  rotate  by  magnets,  and 
magnets  by  currents,  under  the  influence  of  continuous 
electro-magnetic  attraction  and  repulsion.  Let  a  magnet  N  s, 
Fig.  145,  be  weighted  so  as  to  float  upright  in  a  vessel  filled 

FIG.  145. 


with  mercury,  and  let  the  upper  end  of  the  magnet  carry  a 
little  capsule  m  of  mercury,  serving  to  connect  the  magnet 
with  one  pole  of  a  galvanic  battery  by  the  point  z,  and 
yet  leave  it  free  to  rotate  ;  the  magnet  should  be  well  var- 
nished, except  at  its  lower  end.  Let  the  other  pole  of  the 
battery  be  brought  to  the  mercury  near  the  magnet  by  a 
wire  c  :  the  magnet  will  rotate  so  long  as  the  circuit  is 
complete.  The  cause  will  be  obvious  if  we  consider  the 
magnet  to  be  a  kind  of  solenoid,  for  then  a  force  will  act 
between  each  ring  of  the  solenoid  and  the  current  going 
from  the  centre  to  the  circumference,  as  in  the  second  ex- 
periment of  the  last  §.  The  force  in  this  case  will  cause 


296  Electricity  and  Magnetism.       [CHAP.  XXI. 

the  ring  (the  solenoid  or  magnet)  to  rotate,  the  current 
flowing  from  centre  to  circumference  being  fixed. 

If  the  magnet  be  fixed  and  a  little  wire  frame  similar  to 
that  in  Fig.  144  be  pivoted  upon  it  with  the  two  vertical  ends 
p  dipping  into  the  mercury  near  the  magnet,  the  frame  will 
be  caused  to  rotate  by  the  magnet.  This  is  explained  by  the 
third  experiment  of  §  1,  if  we  look  upon  the  magnet  as  a 
solenoid. 

§  3.  The  power  to  be  obtained  from  the  above  arrange- 
ments of  magnets  and  currents  is  so  small  that  they  cannot 
be  employed  to  drive  any  other  apparatus,  and  cannot 
therefore  be  termed  electromotors.  By  alternately  mag- 
netizing and  demagnetizing  electromagnets  we  can  construct 
electromotors  giving  out  as  mechanical  effect  a  considerable 
fraction  of  the  whole  energy  of  the  electric  current.  The 
simplest  electromotor  is  Froment's  rotating  engine.  This 
consists  of  one  or  more  horse-shoe  electromagnets,  A  A,, 
fixed  as  in  Fig.  146,  radially  outside  the  periphery  of  a 
drum,  L»,  capable  of  rotation.  On  the  periphery  of  this 

FIG.  146. 


movable  drum  there  are  a  series  of  soft  iron  bars  01 
armatures,  B  B  B,  etc.  As  the  drum  revolves  it  completes 
a  circuit,  by  suitable  make  and  break  pieces,  sending  a 
powerful  current  through  each  electromagnet  as  each  arma- 
ture approaches  its  poles  within  15°  or  20°:  the  electro- 
magnet then  attracts  the  armature  and  so  drives  the  drum 


CHAP.  XXL]        Electro-magnetic  Engines.  297 

forward.  The  circuit  is  interrupted,  and  the  magnet  there- 
fore unmade,  just  as  the  armature  passes  the  poles  ;  the  drum 
continues  its  rotation  by  inertia  or  by  the  action  of  another 
electromagnet,  until  a  second  armature  approaches  the  poles 
of  the  first  electromagnet,  when  the  circuit  is  made  as 
before.  The  make  and  break  pieces  and  successive  elec- 
tromagnets are  so  arranged  that  the  current  is  not  cut  off 
from  one  circuit  till  it  can  flow  through  the  next.  This  has 
the  double  advantage  of  tending  to  produce  uniformity  in 
the  driving  action  and  of  preventing  the  passage  of  sparks 
when  the  contacts  are  made  and  broken.  These  sparks 
tend  to  burn  the  contacts,  and  gradually  to  prevent  them 
from  closing  the  circuit. 

Another  form  of  electromotor  is  constructed,  resembling 
the  ordinary  beam  steam  engine  ;  the  piston  is  represented 
by  a  magnet  which  is  alternately  sucked  into  a  hollow  coil, 
and  repelled  as  the  current  in  the  coil  is  reversed ;  sometimes 
a  soft  iron  piston  is  used,  which  is  alternately  attracted  and 
set  free. 

§  4.  Much  more  attention  would  be  directed  to  electro- 
motors than  they  have  hitherto  received  were  it  not  for  the 
fact  that  they  are  necessarily  at  least  fifty  times  more  ex- 
pensive to  maintain  in  action  than  the  ordinary  steam 
engine.  Zinc  is  the  cheapest  material  by  the  consumption 
of  which  electricity  is  produced.  The  energy  evolved  by  the 
consumption  of  one  grain  of  zinc  is  only  about  y^th  of 
that  developed  by  the  consumption  of  a  grain  of  coal. 
A  large  fraction  of  the  energy  in  the  case  of  the  zinc  can  be 
converted  into  an  electric  current,  whereas  we  have  not 
yet  discovered  any  means  of  obtaining  the  energy  of  coal 
except  as  heat,  and  we  necessarily  waste  a  great  part  of  this 
heat  in  the  process  of  transforming  it  into  mechanical  energy. 
In  the  transformation  of  energy  into  mechanical  effect  the 
advantage  lies  with  electricity.  The  whole  of  the  energy 
either  of  heat  or  of  an  electric  current  can  never  be 
transmuted  into  mechanical  effect.  In  the  best  steam 


298  Electricity  and  Magnetism.      [CHAP.  XXII. 

engines  not  one  quarter  of  the  heat  is  so  transformed ;  more 
frequently  about  a  tenth  is  so  used.  It  is  probable  that 
larger  fractions  than  these  of  the  total  energy  could  be 
transformed  by  an  electromotor  into  mechanical  effect ;  but 
this  advantage,  even  if  realised,  cannot  nearly  counter- 
balance the  disadvantage  entailed  by  the  cost  of  zinc, 
which  is  20-fold  that  of  coal  weight  for  weight,  and  200- 
fold  that  of  coal  for  equal  quantities  of  potential  energy. 
In  estimating  as  above  that  the  zinc  motor  may  be  only  50 
times  as  dear  as  the  coal  motor,  I  assume  that  the  electro- 
magnetic engine  may  be  four  times  as  efficient  as  the  heat 
engine  in  transforming  potential  into  actual  energy. 


CHAPTER   XXII. 

TELEGRAPHIC   APPARATUS. 

§  1.  THE  instruments  used  in  telegraphy  may  be  divided 
into  two  great  classes  : — I.  Those  which  transmit  signals 
representing  the  alphabet  by  signs  of  a  purely  conventional 
character.  II.  Those  which  transmit  signals  shown  or  re- 
corded in  some  ordinary  printed  alphabet. 

In  the  first  class  the  apparatus  is  simpler,  because  the 
symbols  representing  the  alphabet  are  chosen  with  reference 
to  the  indications  most  easily  produced  by  electricity  in  a 
telegraphic  circuit.  The  advantages  of  the  second  class 
of  instruments  are,  that  the  chances  of  error  which 
result  from  the  translation  of  telegraphic  symbols  into 
ordinary  writing  are  avoided,  and  that  no  special  training 
is  required  to  read  the  messages  as  they  are  received. 
Each  class  is  best  suited  to  a  special  kind  of  work.  For 
the  general  business  of  the  country,  carried  on  by  a 
special  staff,  the  first  class  is  almost  wholly  employed,  and  will 
probably  retain  this  pre-eminence.  For  private  telegraphs 
read  by  untrained  persons,  and  for  large  stations  where 
highly-trained  mechanics  and  electricians  can  be  employed, 


CHAP.  XXII.]         Telegraphic  Apparatus.  299 

the  second  class  of  instruments,  which  show  messages  in  letters 
or  print  them  in  type,  will  probably  also  continue  to  be 
employed. 

Both  classes  may  be  subdivided  into  those  instruments  in 
which  a  galvanic  battery  generates  the  current,  and  those 
in  which  the  current  is  induced  by  a  magneto-electric 
arrangement. 

§  2.  A  telegraphic  circuit,  when  a  battery  is  used,  consists 
of  (i)  an  insulated  wire  connecting  the  transmitting  and 
receiving  stations,  (2)  the  wire  of  the  receiving  apparatus  at 
the  station  where  the  message  is  to  arrive,  (3)  the  earth, 
which  conveys  the  received  current  back  to  the  sending 
station,  (4)  the  sending  batter y,  or  other  rheomotor*  which 
is  alternately  allowed  to  transmit  its  current  into  the  line,  and 
insulated  from  that  line  by  the  manipulator  who  works  the 
sending  apparatus. 

The  sending  apparatus  is  commonly  some  contrivance  for 
making  or  breaking  the  connection  between  the  battery  and 
the  line  ;  so  that  when  the  circuit  is  completed,  its  resistance 
is  the  sum  of  the  resistances  of  the  battery,  the  line,  the 
wire  in  the  receiving  apparatus,  and  the  tract  of  earth  con- 
necting the  two  stations.  When  a  magneto-electric  sender  is 
used  instead  of  a  galvanic  battery,  the  resistance  of  its  coils 
takes  the  place  of  the  resistance  of  the  battery.  In  land  lines 
the  distinctness  of  the  signals  depends,  other  things  being  equal, 
on  the  strength  and  uniformity  of  the  currents  transmitted  ; 
and  in  order  to  save  the  expense  of  employing  batteries  or 
magneto-electric  arrangements  of  great  electromotive  force, 
it  is  desirable  to  keep  the  resistance  of  all  the  parts  low. 
Thus,  the  thicker  the  wire  the  better  will  be  the  signalling 
with  all  classes  of  instruments ;  but  the  size  of  the  wire  is 
of  much  greater  importance  on  long  lines  than  on  short 
ones.  The  larger  the  plates  of  the  battery  the  better,  but 
on  long  lines  the  resistance  of  this  part  of  the  circuit  sinks 

*  Rheomotor  is   the  name  given  by  Professor  Wheatstone  to  any 
apparatus  which  can  generate  an  electric  current. 


300  Electricity  and  Magnetism.      [CHAP.  XXII. 

into  insignificance  in  comparison  with  that  of  the  line.  The 
less  the  resistance  of  the  receiving  apparatus  the  better  ;  but 
this  also  forms  a  small  percentage  of  the  whole  resistance 
on  long  lines.  The  resistance  of  the  earth  between  most 
stations  is  insensible  if  care  be  taken  to  make  the  two  con- 
nexions with  earth  at  the  two  stations  by  large  plates 
buried  in  damp  earth.  Occasionally,  however,  it  may  be 
necessary  to  take  a  wire  a  long  way  from  the  signalling 
station  before  a  suitable  spot  for  a  good  earth  connexion 
can  be  found.  Signals  are  sometimes  stopped  altogether 
by  a  failure  in  the  earth  connexion. 

CLASS  I. 

§  3.  All  signals  are  made  by  the  alternate  transmission 
and  interruption  of  currents,  and  these  currents  may  be  either 
positive  or  negative  ;  that  is  to  say,  they  may  be  sent  from  the 
copper  or  zinc  pole  of  the  battery  into  the  line,  the  other 
pole  of  the  battery  being  necessarily  put  to  earth  at  the 
same  time.  The  following  are  the  elements  out  of  which 
every  telegraphic  alphabet  must  be  compounded  in  Class  I. 

i°.  The  relative  length  or  duration  of  the  currents  sent. 

2°.  The  relative  strength  of  the  currents. 
These   strengths  may  range  from  zero  upwards  through  all 
strengths    of  positive  current,   and   from   zero   downwards 
through  all  strengths  of  negative  current. 

The  simplest  symbols  are  those  which  record  merely  two 
lengths,  one  long  and  one  short ;  and  those  which  record 
merely  two  strengths,  one  positive  and  one  negative.  The 
Morse  alphabet  is  the  standard  example  of  the  former  class, 
and  the  single  needle  alphabet  the  standard  example  of  the 
second  class. 

§  4.  Morse  signals  are  sent  by  a  simple  key,  which  the 
operator  depresses  when  he  wishes  to  send  a  current,  and 
raises  when  he  wishes  to  interrupt  it.  Fig.  147  shows  a 
common  form.  The  insulating  parts  are  generally  made 
of  dry  wood,  the  resistance  of  which  is  amply  sufficient. 


CHAP.  XXII.  J         Telegraphic  Apparatus. 


A  short  depression  or  mere  tap  sends  the  short  ele- 
mentary signal  technically  called  a  dot ;  a  longer  depression 
sends  the  second  elementary  signal  technically  called  a 
dash.  The  Morse  alphabet  is  formed  by  a  combination  of  dots 
and  dashes,  separated  by  equal  intervals.  The  letters  are 

Frc.  147. 


separated  by  longer  pauses,  and  words  by  still  longer  intervals. 
The  following  table  gives  the  Morse  alphabet.    The  short 
lines  are  dots,  the  long  lines  dashes. 


A  -  — 
A  (re)  • 
B  —  - 
C  — - 
1)  —  - 
E  - 
e  -  -  — 

F 

G 

H  -  -  - 


K--- 
L 

M 

N  — - 

a 

Q 

6,  oe 

P 

Q  _ 

R 


S  .  .  - 
T  — 

U 

ii,  ue  - 

V 

\V 

X 

Y . 

2 

Ch 


Full  stop  ( .  ) 

Colon  (  :  ) 

Semi-colon  (  ; ) 

Comma  ( ,  )  

Note  of  interroga-  "\ 
tion  (?)  J' 


2  -  -  — 

3 

4 

5 


Note  of  admi-  "^ 
ration  (!)    J  " 

Hyphen  (-) • 

Apostrophe  ( ' )  - 
Parenthesis  (  —  - 
Inverted  "I 

Commas  ("  ")/ 

6 

8 ' 

9 

o 


;o2 


Electricity  and  Magnetism.     [CHAP.  XXII. 


Bar  of  division  — 

Call  signal — 

Understand  message 

Repeat  message  -  -  — 

Correction  or  rub  out 

End  of  message  -  — •—  • 

Wait 

Cleared  out  and  all  right *  —  -   -  —  • 

Begin  another  line — 

The  positive  and  negative  alphabet  may  be  exactly  similar 
to  the  above  ;  the  dash,  or  long  signal,,  being  replaced  by  a 
mark  on  the  right  side  of  the  paper,  or  by  the  motion  of  some 
index  to  the  right,  and  the  dot  by  a  mark  on  the  left  side, 
or  a  motion  to  the  left. 

§  5.  Ink  marks  similar  to  those  printed  above  are  made 
on  a  long  strip  of  paper  at  the  receiving  end  of  a  line,  by  the 
device  shown  in  Fig.  148. 

FIG.  148. 


Let  M  represent  the  Morse  sending  key ;  L  the  insulated 
line,  reaching  from  the  sending  station  to  the  receiving 
station,  where  the  conductor  is  connected  to  one  end  of 
the  wire  of  an  electro-magnet  R,  the  other  end  of  that  wire 
being  directly  connected  with  E,  the  earth.  Let  A  be  a  soft 
iron  armature  hinged  at  a,  and  having  a  narrow  roller  b  con- 
tinually revolving  in  an  ink  trough  B.  Let  the  strip  of  paper 
p  be  continually  moving  in  the  direction  of  the  an  ows.  Then 
when  M  is  depressed,  making  contact  at  m  with  one  pole  of 
a  battery  c  z,  the  other  pole  of  which  is  to  earth,  a  current 
will  flow  through  the  whole  circuit  and  make  the  core  of  R 
magnetic.  The  end  A  of  the  armature  will  be  depressed,  the 


CHAP.  XXII.]          Telegraphic  Apparatus.  303 

little  roller  pressed  against  the  paper,  and  a  black  mark 
made,  the  length  of  which  will  depend  on  the  rate  at  which 
the  paper  is  moved,  and  the  time  during  which  M  remains 
depressed.  On  raising  the  handle  M  so  that  the  contact  is 
now  made  at  o,  the  current  will  cease  to  flow  ;  the  core  of  R 
will  lose  its  magnetism :  A  will  rise,  pulled  up  by  a  little 
spring,  and  the  ink  mark  will  cease  on  the  paper.  Thus 
a  short  depression  of  M  will  make  a  short  mark  or  dot ; 
a  long  depression  of  M  will  make  a  long  mark  or  dash.  The 
handle  M  is  in  the  diagram  shown  in  a  neutral  position, 
making  contact  neither  at  o  nor  at  m  ;  in  practice  it  is  never 
in  this  position,  but  makes  contact  at  o  when  not  depressed 
by  hand. 

Fig.  149  shows  a  complete  Morse  ink  writer  as  made  by 
Messrs.  Siemens  Brothers.  The  following  is  a  description 
of  the  instrument  almost  in  their  own  words  : — E  is  the 
electro-magnet,  through  which  the  received  current  passes. 
N  is  a  handle  by  which  the  clockwork  is  wound  up. 

The  clockwork  placed  inside  the  instrument  turns  a  small 
milled  roller  w,  and  the  printing  disc  D.  The  friction  rollei 
Wj  is  pressed,  by  means  of  a  spring  v,  upon  w,  and  turns 
with  it. 

The  disc  of  telegraph  paper  s  is  placed  upon  the  horizontal 
wheel  P,  which  turns  on  a  hardened  pivot  a.  Horizontal 
wheels  for  paper  were  first  introduced  by  Mr.  Stroh,  and 
are  much  superior  to  vertical  wheels.  The  end  of  the  strip 
of  paper  is  led  round  the  roller  s1,  turning  on  a  vertical 
axis,  thence  under  the  roller  s11,  over  the  roller  s,  and  under 
the  small  steel  roller  /",  where  it  is  struck  by  the  printing 
disc  D,  on  the  armature  e  being  attracted  by  the  electro- 
magnet E.  From  the  small  roller  i  the  strip  of  paper  passes 
between  the  friction  rollers  w  and  Wj,  which,  when  they  re- 
volve, draw  the  paper  forward  in  the  direction  of  the  arrows. 

The  roller  wt  can  be  lifted  by  the  small  handle  x ;  and  it 
will  be  found  convenient  to  lift  it  in  this  manner  when  in- 
troducing the  paper  between  the  friction  rollers  w  and  w,. 


304 


Electricity  and  Magnetism.      [CHAP.  XXII. 

FIG.  149- 


CHAP.  XXII. ]         Telegraphic  Apparatus.  305 

A  A  is  a  brass  vessel  for  holding  a  supply  of  printing-ink, 
the  opening  to  which  for  putting  in  the  ink  is  supplied  with 
a  cover  c  to  prevent  dust  from  getting  into  it;  the  vessel 
terminates  in  an  open  cup  or  trough  b  b,  in  which  the  print- 
ting  disc  D  revolves.  The  vessel  A  A  is  fastened  to  the  side 
of  the  apparatus  by  means  of  a  screw  with  a  milled  head  c, 
so  that  it  can  be  easily  removed  for  refilling  or  cleaning. 
The  spindle  on  which  the  printing  disc  D  is  fastened  revolves 
in  an  eye  at  the  end  of  the  continuation  h  of  the  printing 
lever  H  H.  The  spindle  is  made  to  revolve  by  being  joined, 
at  the  end  furthest  from  the  printing  disc,  by  a  species  of 
universal  joint,  to  the  end  of  a  short  spindle  carrying  a  cog- 
wheel in  gear  with  the  clockwork.  The  printing  disc  is  thus 
kept  revolving,  although  free  to  follow  the  motions  of  the 
printing  lever. 

Should  it  be  wished  to  stop  the  clockwork  of  the  instru- 
ment, the  handle  Q  must  be  pushed  to  the  right,  by  which 
the  spring/  is  pressed  against  the  small  metal  collar^  of 
the  regulator  t.  The  release  of  the  clockwork  is  effected  by 
moving  the  handle  Q  in  the  opposite  direction. 

The  cores  of  the  electro-magnet  are  of  soft  iron,  united 
by  a  cross-bar  and  surrounded  by  the  wire  coils.  The 
lever  H  H  moving  between  the  points  2  and  3  of  the 
screws  m  and  m^  carries  on  one  arm  an  armature  of  iron  <?, 
and  at  the  other  end  the  continuation  /i,  in  an  eye  at  the 
end  of  which  revolves  the  end  of  the  spindle  which  carries 
the  printing  disc  D. 

The  contact  screws  m  and  m}  limit  the  play  of  the  print- 
ing lever  H  H.  In  order  to  draw  the  lever  back  to  its  normal 
position  as  soon  as  a  current  has  ceased,  a  spring  k  is  pro- 
vided, the  degree  of  tension  of  which  can  be  regulated  by 
means  of  the  nut  o.  Another  adjustment  has  been  adopted, 
in  addition  to  the  above,  by  which  the  electro-magnet  E  has 
been  made  moveable,  and  can  be  raised  or  lowered  by 
means  of  the  milled  headed  screw  n,  thereby  increasing  or 


306 


Electricity  and  Magnetism.      [CHAP.  XXII. 


decreasing  the  distance  between  the  cores  of  the  magnets 
and  the  armature  e  of  the  printing  lever  H  H. 

When  the  circuit,  Fig.  148,  is  closed  at  m  a  current  from  the 
copper  of  the  distant  battery,  after  traversing  the  line,  enters 
the  printing  instrument  R,  passes  through  the  coils  E  of  the 
electro-magnet,  Fig.  149,  and  leaving  the  instrument  returns 
through  the  earth  to  the  zinc  of  the  distant  battery.  As 
long  as  the  current  lasts,  the  iron  cores  are  converted  into 
magnets,  the  free  ends  of  which  will  attract  the  armature 
e  and  thus  set  the  printing  lever  H  H  in  motion.  The  con- 
tinuation h  of  the  printing  lever  H  H  consequently  presses 
the  disc  D  against  the  paper  band,  upon  which  it  produces 
a  dot  or  a  dash,  according  to  the  length  of  time  during 
which  the  armature  is  attracted  by  the  cores. 

There  are  many  modes  of  receiving  and  recording  the 
Morse  signals  besides  that  just  described.  In  many  old 
instruments  the  roller  ^,  Fig.  148,  is  replaced  by  a  mere 
steel  pointer  or  style,  which  makes  a  little  indented  line  when 
pressed  on  the  paper  by  the  depression  of  A.  In  Bain's 
chemical  telegraph,  Fig.  150,  the  electro-magnet  R  is  wholly 
dispensed  with.  The  depression  of  M  sends  a  positive  current 

FIG.  150. 
L 


through  R,  c,  and  L,  and  then  at  the  receiving  station 
through  a  steel  style  <:,  pressing  on  a  band  of  paper/, 
which  has  been  soaked  in  a  mixture  of  equal  parts  of  satu- 
rated solutions  of  ferrocyanide  of  potassium  and  nitrate  of 


CHAP.  XXIL]          Telegraphic  Apparatus.  307 

ammonia.  The  current  next  flows  to  r  and  through  m  to 
earth,  the  handle  of  m  being  raised.  The  diagram  shows 
the  connections  so  arranged  that  all  signals  can  be  sent  from 
either  end.  At  the  receiving  station  the  keys  M  or  m  make 
contact  at  o  or  o.  Prussian  blue  is  deposited  so  long  as  the 
current  passes  through  the  paper3  and  thus  the  long  and 
short  signals  are  recorded  by  short  or  long  blue  marks. 
There  should  be  a  slight  excess  of  carbonate  of  ammonia  in 
the  solution  of  nitrate. 

Sometimes  the  Morse  signals  are  indicated  to  the  ear  or 
eye  without  being  recorded.  Thus,  even  if  the  paper  at  P, 
Fig.  148,  be  removed,  the  mere  sound  of  the  armature  as  it 
rises  and  falls  is  intelligible  to  the  ear  of  a  skilled  operator. 
The  sounder,  as  it  is  called,  is  coming  into  extensive  use  and 
consists  of  a  Morse  receiver  without  clockwork  or  paper  or 
inking  roller.  The  sound  is  produced  by  the  tapping  of  the 
lever  H,  Fig.  149,  against  the  stops  m  and  0/t.  The  mere  de- 
flection of  a  galvanometer  needle,  included  in  the  circuit  at 
R,  will  be  equally  intelligible  to  the  eye.  It  is  only  necessary 
to  make  the  needle  light  and  confine  its  motion  within  narrow 
limits,  so  that  each  current  in  passing  produces  a  single  well- 
marked  depression  lasting  for  a  longer  or  shorter  time,  and 
not  a  series  of  unchecked  oscillations. 

§  6.  The  simplest  form  of  receiving  instrument  for  posi- 
tive and  negative  signals  is  a  little  galvanoscope,  the  index 
of  which  can  deflect  only  a  short  distance  to  right  or  left  of 
its  zero,  being  checked  by  stops.  The  inside  of  one  of 
these  instruments  is  shown  in  Fig.  151.  I  i  are  the  coils 
fastened  to  the  back  of  a  little  door  which  opens  to  allow  the 
works  to  be  got  at ;  A  is  a  support  in  which  one  pivot  of  the 
needle  works  ;  N  P  are  the  keys  used  in  sending;  the  needle 
s  N  and  pointer  a  b  are  shown  in  Fig.  152.  The  key  by  which 
the  positive  and  negative  signals  are  sent  from  one  and  the 
same  battery  is  better  shown  in  Fig.  153.  L  and  E  are  two 
springs  connected  respectively  with  the  line  and  with  earth. 
They,  when  untouched  by  the  hand,  press  against  the  upper 

x  2 


3°S 


Electricity  and  Magnetism.      [CHAP.  XXII. 


bar  c,  which  is  connected  with  the  copper  pole  of  a  battery. 
Either  spring  can  be  depressed  by  the  finger  so  as  to  come 
in  contact  with  the  bar  z,  which  is  connected  with  the  zinc 
pole  of  the  battery.  If  L  is  depressed,  a  negative  current 
flows  into  the  line ;  if  E  is  depressed,  a  positive  current  flows 
into  the  line.  The  galvanoscope  at  the  other  end  is  so  con- 
nected that  the  depression  of  the  left-hand  key  causes  a  de- 
flection to  the  left ;  a  depression  of  the  right-hand  key  a 
deflection  to  the  right.  The  form  of  galvanoscope  used  is 

FIG.   i5T. 


called  the  single  needle  instrument,  and  the  alphabet  the  single 
needle  code.  The  Morse  code  given  above  is  often  used, 
a  dot  being  a 'deflection  to  the  right  and  a  dash  a  deflection 
to  the  left. 

Sir  Charles  Bright  introduced  the  bell  instrument  as  a 
substitute  for  the  single  needle.  His  instrument  contains 
two  bells  struck  by  the  depression  of  the  armatures  of  two 
electro-magnets,  one  working  each  bell.  Each  electro-magnet 


CHAP.  XXII. ]          Telegraphic  Apparatus.  309 

was  worked  by  its  own  relay ;  one  of  the  relays  worked 
when  a  positive  current  was  received,  and  the  other  when 
the  received  current  was  negative.  This  instrument  is  falling 
into  disuse. 

§  7.  The  connections  shown  above  are  most  suitable  for 
comparatively  short  lines.  On  longer  lines  more  complex 
arrangements  are  generally  adopted,  involving  the  use  of 
relays.  The  Relay  is  an  instrument  which  retransmits  the 
original  signal  from  a  fresh  battery:  it  may  be  used  either 
to  send  this  signal  to  a  distance  along  a  second  section 
of  line,  or  simply  to  send  a  strong  current  from  a  local 

FIG.  152.  FIG.  153. 


battery  through  the  receiving  instrument.  The  current 
received  from  a  distance  is  often  so  diminished  by  leak- 
age that  it  is  insufficient  to  work  the  electro-magnet  which 
marks  the  paper,  or  to  give  legible  or  audible  signals, 
and  yet  it  may  be  sufficiently  strong  to  move  an  armature 
with  sufficient  force  alternately  to  make  and  break  an 
electric  contact,  and  thus  indirectly  to  work  the  receiv- 
ing or  recording  instrument  Fig.  154  shows  the  con- 


3io 


Electricity  and  Magnetism.      [CHAP.  XXII. 


nection  for  a  Morse  system  with  relays  at  each  end,  worked 
by  single  currents. 

Corresponding  parts  at  the  two  stations  are  indicated  by 
the  same  letters,  capitals  being  used  for  one  station  and 
italics  for  the  other.  R  is  the  relay,  and  c  z  the  sending 
battery;  R!  is  the  Morse  instrument,  and  Cj  z{  the  local 
battery  used  to  work  it.  The  depression  of  the  key  m 
making  contact  at  o  sends  a  positive  current  through  the 
line  L  to  M,  and  through  the  contact  P  to  the  electro-magnet 
R  of  the  relay  and  thence  to  earth.  The  electro-magnet  R 
attracts  the  armature  of  the  relay,  making  contact  at  N  and 

FIG.   154. 


thus  sending  a  positive  current  through  R,,  the  electro-magnet 
of  the  recording  instrument. 

Obviously  RJ  might  be  at  a  station  160  miles  from  R,  in 
which  case  L!  would  be  the  second  line,  and  the  portion 
of  the  circuit  from  Zj  to  R!  the  earth. 

Relays  are  constructed  so  that  a  very  slight  difference  in 
the  strength  of  a  current  determines  whether  the  moveable 
tongue  or  armature  makes  contact  at  N,  or  rests  against 
an  insulated  stop.  Care  is  also  taken  to  provide  such  adjust- 
ments that  the  tongue  may  be  made  to  move  with  any  desired 
strength  of  current :  thus  the  relay  may  be  set  so  that  with  zero 
strength  the  tongue  rests  on  the  stop  and  makes  contact  when 
the  current  reaches  the  strength  unity,  or  it  may  be  set  so  that 
it  rests  against  the  stop  when  the  current  has  a  strength  100, 
and  makes  contact  when  the  current  has  a  strength  101. 


CHAP.  XXII.]         Telegraphic  Apparatus.  3 1 1 

Relays  are  also  often  made  so  that  the  tongue  moves  only 
with  a  current  of  one  sign,  remaining  unaffected  by  a  current 
of  the  opposite  sign  ;  the  core  Of  the  electro-magnet  may  in 
this  case  be  a  hard  steel  magnet,  the  polarity  of  which  is 
never  reversed  by  the  currents  received.  Other  relays 
are  made  so  that  when  the  tongue  has  once  been  de- 
flected to  make  contact,  it  will  not  return  until  a  reverse 
current  has  been  sent  through  it.  The  best  known  form  of 
this  species  is  the  polarized  relay  made  by  Messrs.  Siemens, 
and  shown  in  Fig.  155.  s  is  the  Fic  iss 

south  pole  of  a  hard  steel  magnet, 
the  north  pole  of  which  is  bifur- 
cated and  ends  in  the  two  pieces 
n  ;2j,  between  which  the  tongue  a 
of  the  relay  oscillates,  pivoted  at 
D.  The  coils  are  wound  round  the 
two  north  branches  of  the  magnet 
in  opposite  directions,  so  that  a 
current  in  one  direction  tends 
to  make  nl  north  and  n  south, 
while  the  reverse  current  would 

make  ;z,  south  and  n  north.     The  tongue  «,  made  of  soft 
iron,  becomes  a  south  pole  by  contact  with  s  s. 

Relays  can  be  arranged  so  as  to  send  positive  and 
negative  currents  corresponding  to  positive  and  negative 
currents  received. 

The  Morse  ink -writer  can  easily  be  arranged  so  as  to  act 
like  a  relay,  the  armature  being  employed  to  make  the 
necessary  contacts  instead  of  to  mark  paper.  With  instru- 
ments of  this  class  Messrs.  Siemens,  on  the  Indo-European 
line,  work  from  London  to  Teheran,  a  distance  of  3,800 
miles,  without  any  retransmission  by  hand.  There  are  five 
relay  stations  in  this  circuit. 

§  8.  In  ordinary  Morse  signals  and  in  all  others  where  only 
one  current  is  absolutely  required,  there  is  nevertheless 
some  advantage  in  using  the  negative  current  to  draw  back 


3 1 2  Electricity  and  Magnetism.      [CHAP.  XX II. 

the  armature  and  so  terminate  each  signal.  This  system 
was  introduced  by  Mr.  Varley.  It  considerably  simplifies 
the  adjustment  of  the  relays  and  has  other  advantages. 
Where  these  reverse  currents  are  not  used,  the  relay  tongue 
must  be  pulled  back  by  a  spring  or  by  magnetic  attraction, 
and  their  adjustments  require  to  be  continually  altered. 
This  spring  requires  continual  adjustment  to  suit  the  strength 
of  the  received  current,  which  varies  much  during  each  day 
as  the  insulation  of  the  line  varies.  With  a  polarized  relay 
and  reverse  currents,  no  such  adjustment  is  required,  be- 
cause the  positive  and  negative  currents  decrease  simul- 
taneously; and  if  there  were  no  earth  currents,  a  good 
polarized  relay  once  set  for  reverse  currents  would  never 
require  to  be  touched  ;  practically,  all  relays  require  adjust- 
ment from  time  to  time.  Earth  currents  are  currents 
flowing  along  the  line,  not  sent  by  the  batteries,  but  de- 
pending either  on  a  difference  of  potential  between  the 
earth  at  the  two  stations  or  on  induction  from  passing  clouds. 
Currents  often  flow  for  hours  in  one  direction  through  the 
lines,  and  the  signalling  currents  are  superposed  on  these 
earth  currents ;  the  relays  then  have  to  be  set,  so  that  when 
no  signal  currents  are  passing  the  armature  is  attracted  more 
strongly  by  one  armature  than  by  the  other,  and  the  amount 
of  this  bias  must  be  regulated  as  the  earth  currents  vary. 

§  9.  With  the  connections  as  shown  in  Fig.  154,  although 
no  current  is  sent  direct  from  the  battery  through  the  home 
relay  circuit,  every  signal  sent  causes  the  relay  at  the  sending 
station  to  work,  if  the  line  is  long  and  well  insulated,  or 
if  it  includes  many  miles  of  underground  or  submarine  wires. 
This  action  is  due  to  the  statical  charge  which  accumulates 
on  the  line  L.  When  contact  is  made  by  the  key  M  at  o, 
the  line  L  becomes  statically  charged.  When  contact  is 
broken  at  o,  and  made  at  P,  part  of  this  statical  charge  flows 
to  earth  through  the  relay  R,  the  other  portion  flowing  on 
through  the  distant  relay  r-}  thus  the  key  M  as  it  makes  and 
breaks  contact  causes  intermittent  currents  to  flow  through 


CHAP.  XXII.]          Telegraphic  Apparatus.  313 

the  home  relay  which  will  work  the  local  Morse  instrument RP 
This  action  is  not  only  unnecessary,  but  is  detrimental, 
because  the  currents  returned  in  this  way  are  often  so 
strong  as  to  alter  the  permanent  or  residual  magnetism  of  the 
relay,  which  then  requires  readjustment  when  signals  begin 
to  arrive  from  the  distant  station,  and  moreover  the  local 
battery  c}  z{  is  put  in  action  by  these  return  currents  when 
not  required.  The  return  current  is  especially  great  when 
any  portion  of  the  line  L  is  formed  of  wire  coated  with 
india-rubber  or  gutta-percha,  because  lines  so  formed 
have  a  much  larger  electrostatical  capacity  than  the 
ordinary  aerial  land  line.  Where  this  inconvenience 
exists,  each  station  may  be  provided  with  an  apparatus 
called  a  switch,  by  which  the  connections  are  altered  at 
will,  so  that  when  the  station  M,  fig.  154,  for  instance,  is 
sending  the  relay,  R  is  not  in  the  circuit  between  p  and  E, 
which  points  are  then  directly  connected. 

The  sending  key  M  is  sometimes  so  made  as  to  put  the 
line  to  earth  for  a  short  time  between  the  two  positions 
where  it  makes  contact  respectively  with  o  and  p. 

A  still  better  arrangement  for  discharging  may  be  em- 
ployed, in  which  the  action  of  the  current  sent  from  the 
home  station  puts  p  to  earth  by  means  of  a  separate  relay, 
and  keeps  p  to  earth  by  residual  magnetism  for  a  very  short 
time  after  the  key  M  has  broken  contact  at  o  and  made  con- 
tact at  P.  With  this  arrangement  the  distant  station  can  at 
will  interrupt  the  sender. 

10.  The  following  points  must  be  attended  to  in  the 
construction  of  telegraphic  apparatus  : — 

The  core  of  the  electro-magnet  should  be  arranged  so  that 
its  magnetism  changes  rapidly  at  the  commencement 
or  cessation  of  a  current ;  otherwise  rapidly  alternat- 
ing changes  produced  by  rapid  signals  will  not  be  regis- 
tered by  the  armature.  With  this  object,  if  soft  iron  is 
used,  the  mass  should  not  be  great ;  the  core  should  be 
hollow,  and  split  longitudinally;  and  the  iron  should  be 


Electricity  and  Magnetism.      [CHAP.  XXII. 

carefully  selected  with  as  little  coercive  force  as  possible. 
The  highly  magnetized  cores  of  polarized  relays  gain  and 
lose  the  small  increments  of  magnetism  due  to  feeble 
currents  with  less  delay  due  to  coercive  force  than  is  ex- 
perienced with  soft  iron.  The  coercive  force  in  the  arma- 
tures is  another  source  of  delay  in  rapidly  alternating 
signals.  These  armatures  should,  therefore,  be  made 
light,  and  must  not  pass  through  very  different  states  of 
magnetization.  If  allowed,  for  instance,  actually  to  touch  the 
core  of  the  electro-magnet,  they  become  so  highly  mag- 
netized that  when  the  electro-magnet  is  weakened  by  the 
cessation  of  the  current,  they  often  adhere  to  the  core  under 
the  influence  of  residual  magnetism,  requiring  a  very  strong 
spring  to  pull  them  back,  and  consequently  a  very  powerful 
current  to  pull  them  against  the  spring  to  the  electro-magnet. 
The  most  delicate  relay  is  that  in  which,  other  things 
being  equal,  the  armature  moves  in  a  nearly  constant 
magnetic  field,  which  is  alternately  weakened  and  strength- 
ened by  the  received  current.  The  alteration  produced  in 
the  magnetic  field  of  the  electro-magnet  by  the  passage  of  a 
current  should,  however,  be  the  greatest  which  that  current 
can  produce,  and  this  condition  requires  that  the  iron  or 
steel  core  should  not  be  very  small ;  moreover,  some  little 
pressure  must  be  exerted  at  the  contacts,  or  the  tongue  of 
the  relay  will  be  made  to  tremble  by  the  mere  passage  of  the 
local  current,  which  exercises  a  repulsion  on  itself ;  to  obtain 
the  necessary  force,  the  armature  must  have  considerable 
bulk:  these  two  last  conditions  are  antagonistic  to  those  first 
mentioned,  and  experiment  alone  can  determine  the  best 
proportions.  The  form  of  the  electro-magnet  should  be 
such  as  to  give  the  strongest  and  most  uniform  field  possible 
with  a  given  intensity  of  magnetization.  This  condition  is 
entirely  violated  in  the  common  relay  or  ink-writer,  where 
the  armature  stretches  across  the  poles  of  an  ordinary  horse- 
shoe magnet.  It  is  much  more  nearly  complied  with  in  the 
Siemens  polarized  relay  described  above.  The  form  of 
the  iron  or  steel  core  and  the  distribution  of  the  core  on  the 


CHAP.  XXII.]         Telegraphic  Apparatus.  315 

magnet  should  be  such  as  to  give  the  maximum  intensity  of 
magnetization  per  cubic  centimetre  of  core  consistent  with  a 
given  current  passing  through  a  given  length  of  wire.  This 
condition  is  probably  very  imperfectly  fulfilled  by  any 
relay  yet  constructed. 

The  mass  of  the  armature  should  be  s*o  distributed  that  its 
moment  of  inertia  may  be  the  smallest  that  is  consistent 
with  the  necessary  weight  of  the  armature  and  position  of 
the  pivots  ;  any  increase  in  the  moment  of  inertia  pro- 
duces a  proportional  diminution  in  the  angular  velocity 
with  which  the  tongue  will  move  under  a  given  force,  and 
the  rate  at  which  a  relay  will  work  depends  on  this  angular 
velocity.  If  the  moment  of  inertia  be  doubled,  the  force 
remaining  the  same,  the  angular  velocity  acquired  in  a 
given  time  will  be  halved,  and  the  angle  traversed  in  that 
time  will  be  halved ;  but  to  traverse  the  same  angle,  i.e.  to 
pass  from  one  contact  to  the  other,  will  not  require  double 
the  time,  but  only  1*414  times  the  time  required  by  the 
lighter  armature,  because  1-414  =  ^2.  The  moment  of 
inertia  is  the  sum  of  the  products  of  the  weight  of  each 
particle  into  the  square  of  its  distance  from  the  pivot  round 
which  the  mass  rotates  :  it  is  therefore  not  only  desirable, 
when  rapid  motion  is  to  be  produced  by  a  weak  force,  that 
the  weight  should  be  small,  but  also  that  it  should  be  near 
the  pivots. 

No  harm  is  done,  however,  by  putting  the  pivots  far  from 
the  points  of  contact,  because  we  thereby  diminish  the  angle 
through  which  the  armature  has  to  move  between  the 
contacts ;  so  that  if  we  halve  the  angle  and  double  the 
moment  of  inertia,  the  one  change  exactly  compensates  the 
other. 

The  wire  on  the  electrormagnet  (or  in  the  coil  of  the  single 
needle  instrument)  should  have  a  moderate  resistance  re- 
latively to  that  of  the  whole  circuit  : 1  thus  on  short  lines  a 

1  One  authority  says  ~  of  the  resistance  of  the  whole  circuit ;  this 
seems  very  large. 


3 1 6  Electricity  and  Magnetism.      [CHAP.  XXII. 

thick,  short  wire  should  be  used  for  the  electro-magnet ;  but 
on  long  lines,  relays  with  long,  thin  wires  are  required.  The 
reason  for  this  is  the  same  as  that  for  using  galvanometers 
with  long  coils  to  test  insulation,  and  galvanometers  with 
short  coils  to  observe  currents  in  circuits  otherwise  of  small 
resistance.  The  colnmon  single  needle  instruments  have  a 
resistance  of  about  200  ohms,  the  coil  being  made  of  No.  35 
wire. 

The  direct  ink-writer  used  for  short  lines  may  be  coiled 
with  No.  35  wire  (0*005  inch  diameter),  and  have  a 
resistance  of  about  500  ohms. 

The  electromagnets  in  local  instruments  (no  line  wire  on 
circuit)  are  made  with  wires  of  from  "022  inch  to  0*012 
inch  diameter  (Nos.  24  to  30). 

A  Siemens  polarised  relay  may  be  made  with  No.  40 
copper  wire,  and  have  a  resistance  of  500  to  700  ohms. 
These  relays  sometimes  have  a  resistance  of  3,500  ohrns. 

All  contacts  must  be  made  by  platinum  points,  platinum 
being  the  only  metal  which  is  not  oxidized  or  dirtied  by  the 
passage  of  the  little  spark  which  accompanies  the  making 
and  breaking  of  the  circuit.  This  spark  wears  out  even  the 
platinum  contact  pieces  in  time :  it  may  be  avoided  by 
connecting  permanently  the  two  contact  pieces  through  a 
resistance  so  large  that  the  current  passing  when  contact  is 
broken  is  small  enough  not  to  be  injurious.  The  same 
object  is  gained  by  placing  a  small  condenser  between  the 
contact  pieces,  each  contact  piece  being  connected  with  one 
of  the  two  armatures. 

§  11.  In  place  of  a  voltaic  battery,  a  magneto-electric 
arrangement  may  be  employed  to  send  currents.  Thus  a 
Siemens  armature  worked  by  hand  may  be  employed  to  send 
Morse  signals,  the  motions  of  the  hand  being  similar  to  those 
required  for  the  Morse  key.  The  depression  of  a  handle 
moves  the  armature  in  one  direction,  and  sends,  say,  a  posi- 
tive current,  which  by  a  polarized  relay  causes  an  ink- writer 
to  begin  marking  the  paper.  So  long  as  the  armature 


CHAP.  XXII. ]         Telegraphic  Apparatus.  317 

and  handle  remain  depressed  the  ink-writer  continues  to 
mark,  though  no  current  is  flowing  through  the  relay,  the 
tongue  of  which  is  held  over  by  the  permanent  magnetism 
of  its  magnet ;  when  the  handle  is  raised  and  the  armature 
moved  back  to  its  original  position,  another  short  current  is 
sent  in  the  opposite  direction  to  the  first.  This  second 
current  throws  back  the  tongue  of  the  relay,  and  the  ink- 
writer  ceases  to  mark.  The  current  produced  is  the  equi- 
valent of  the  power  employed  to  work  the  armature ; 
considerable  force  must  therefore  be  exerted  to  send  a 
current  suitable  for  a  long  circuit.  Other  magneto-electric 
arrangements  are  used  to  send  +  and  —  signals  for  the 
single  needle  receiver.  The  induced  currents  are  of  very 
short  duration  ;  and  hence,  although  the  E.  M.  F.  which  pro- 
duces them  may  easily  be  made  much  greater  than  that  of 
the  batteries  usually  employed  to  signal,  yet  the  actual 
quantity  of  electricity  transmitted  for  each  signal  is  generally 
much  less  than  is  sent  by  a  battery. 

On  a  long  line  the  received  current  is  longer  in  duration 
than  the  sent  current,  and  proportionately  feebler.  On  a 
short  line  the  received  current  and  that  sent  are  both  so 
short,  that  even  when  strong  they  may  fail  to  move  an 
armature  which  would- work  freely  with  a  feebler  current 
prolonged  for  a  longer  time.  The  E.  M.  F.  produced  by  the 
magneto-electric  arrangement  is  so  great  near  the  sending 
station,  that  the  leakage  is  much  greater  in  proportion  to 
the  whole  quantity  of  electricity  sent  than  when  a  battery  is 
used.  This  would  not  be  the  case  if  the  resistance  of  the 
faults  where  electricity  escapes  followed  Ohm's  law,  but  the 
resistance  of  faults  seldom  follows  Ohm's  law.  More  es- 
pecially surface  conduction,  which  is  the  chief  cause  of  leak- 
age on  land  lines,  allows  much  more  than  double  the  current 
to  pass  when  the  E.  M.  F.  is  doubled.  On  underground  or 
submarine  lin£S  the  high  potential  produced  for  a  short 
time  by  the  magneto-electric  sender  tends  to  send  minute 
sparks  through  the  insulating  material,  and  so  to  cause  faults. 


318  Electricity  and  Magnetism.     [CHAP.  XXII. 

Magneto-electric  senders,  owing  to  the  above  causes,  are 
not  much  used  on  long  or  important  lines. 

§  12.  The  simple  Morse  or  +  and  —  key  can  be  worked 
at  the  rate  of  from  twenty-five  to  thirty-five  words  per  minute 
by  a  skilled  operator.  Receiving  instruments  can,  however, 
record  even  more  than  100  words  per  minute  (of  five  letters 
each).  Automatic  transmitters  have  therefore  been  adopted 
in  which  the  messages  are  prepared  by  several  operators, 
being  represented  by  punched  paper  or  metal  types,  and 
these  types  or  paper  strips  passing  through  the  transmitter 
determine  the  required  succession  of  currents.  Sir  Charles 
Wheatstone's  automatic  transmitter  is  the  most  successful 
yet  used.  In  this  instrument  the  messages  are  represented 
by  three  rows  of  holes  in  a  strip  of  paper.  For  +  and  — 
signals  a  hole  on  the  right-hand  side  represents  a  +  signal  or 
dot,  a  hole  on  the  left-hand  side  a  —  signal  or  dash.  Uni- 
formly spaced  central  holes  serve  to  move  the  paper  on  at  a 
constant  speed.  The  right  and  left-hand  holes  determine  the 
contacts  made  and  signals  sent  very  rnuch  as  the  cards  in  a 
Jacquard  loom  determine  the  pattern  in  woven  stuff.  The 
contacts  are  determined  by  the  position  of  two  little  plungers, 
which  are  either  kept  down  by  the  unpunched  paper  or  come 
up  through  the  holes.  Whenever  a  plunger  rises  through  a  hole 
a  current  is  sent  into  the  line ;  a  -f  current  when  the  hole 
is  on  the  right  side ;  a  —  current  when  the  hole  is  on  the 
left  side.  The  contacts  are  pressure  contacts,  with  a  slight 
slip  at  the  moment  of  making  contact,  which  are  superior  to 
any  contact  in  which  the  surfaces  merely  slide  one  on  the 
other.  By  a  somewhat  more  complex  arrangement  of 
similar  character,  the  long  and  short  Morse  signals  are 
sent.  A  full  description  of  this  instrument  is  given  in  the 
Fifth  Edition  of  Mr.  R.  S.  Culley's  Hand-book  of  Prac- 
tical Telegraphy. 


CHAP.  XXIL]         Telegraphic  Apparatus.  3 1 9 

CLASS  II. 

§  13.  The  elementary  signals  used  in  those  telegraphic 
systems  which  show  or  print  letters  are  produced,  as  in 
Class  I.,  by  the  alternate  transmission  or  interruption  of 
currents, .  sometimes  all  of  one  sign,  and  sometimes  both 
positive  and  negative  ;  but  these  transmissions  and  interrup- 
tions are  not  themselves  the  subject  of  direct  observation  or 
record  :  they  are  used  to  work  the  escapement  of  clockwork 
in  what  may  be  termed  '  step  by  step '  instruments,  or  to 
connect  synchronous  actions  in  the  sending  and  receiving  in- 
struments, which  are  driven  with  similar  motions  at  the  two 
ends  of  the  line. 

The  *  step  by  step '  instruments  sometimes  print  the 
messages,  but  more  frequently  show  the  required  letters  in 
succession  on  a  dial.  The  synchronous  instruments  all 
print  the  letters,  but  they  effect  this  by  various  distinct  in- 
ventions, the  more  striking  of  which  are  Hughes's,  Caselli's, 
and  Bonelli's. 

All  '  step  by  step  '  instruments  are  very  much  alike.  A 
ratchet  wheel  on  an  axis  bearing  the  pointer  is  worked  by  a 
propelment  which,  as  each  current  passes,  turns  the  ratchet 
through  a  segment  of  a  circle  corresponding  to  one  tooth  or 
half  a  tooth  of  the  ratchet.  Fig.  156  shows  a  form  now  made 
by  Messrs.  Siemens  Brothers,  and  very  similar  to  that  first 
introduced  by  Sir  Charles  Wheatstone  :  n  s  are  two  poles  of 
a  polarized  electro-magnet,  similar  to  that  used  in  their  relay 
(§10  above).  The  soft  iron  tongue  T  works  between  these, 
pivoted  at  /,  being  attracted  to  s  by  one  current,  and  to  n  by 
the  reverse  current.  The  tongue  T  carries  at  its  other  extremity 
one  end  of  the  axis  of  the  ratchet  wheel  D,  having  thirteen 
teeth ;  the  other  end  of  the  axis  is  on  a  fixed  bearing,  and 
carries  the  pointer.  The  play  of  T  is  limited  by  two  stops, 
q,  qlt  and  the  rotation  of  the  ratchet  is  determined  by 
two  stops/,/,,  and  four  springs,  h,  h\,  /i2,  //3,  two  of  which,  h 
and  /*p  have  a  catch  at  their  end,  adapted  to  hold  the 


320 


Electricity  and  Magnetism.      [CHAP.  XXII. 


ratchet.  The  tongue  T  is  shown  drawn  towards  n ;  the  ratchet 
is  locked  by  the  spring  h,  so  that  it  cannot  turn  to  the  right 
neither  can  it  turn  to  the  left,  because  it  is  locked  by  the  stop 
/.  The  position  of  the  pointer  is  therefore  perfectly  definite. 

FIG.  156. 


The  next  current  received  will  attract  T  to  s  •  the  spring  h 
will  turn  the  ratchet  ^  of  a  revolution,  and  it  will  then  be 
locked  by  the  spring  hl  and  the  stop/!;  the  following  current 
will  turn  the  ratchet  an  equal  distance  by  moving  it  towards 
«,  and  thus  each  alternate  current  will  carry  the  pointer 
forward  by  ^th  of  a  revolution  over  the  dial,  on  which  there 
are  twenty-five  letters  and  one  blank. 

These  thirteen  positive  and  thirteen  negative  currents  will 
cause  the  index  to  make  one  complete  revolution.  Let  us 
assume  that  the  index  is  at  the  letter  A,  then  one  current  will 
move  the  index  to  the  letter  B,  three  currents  more  will  move 
it  to  E,  and  seven  currents  will  send  it  to  L  ;  by  sending  the 
right  number  of  currents  and  then  pausing  for  an  instant,  the 
index  will  be  made  to  travel  from  letter  to  letter,  and  to  pause 
at  each  letter  required  to  be  read.  The  index  may  be  driven 
by  clockwork  and  the  teeth  of  an  escapement  wheel  liberated 


CHAP.  X  X 1 1.  ]          Telegraphic  Apparatus.  3  2 1 

by  the  currents,  or  the  escapement  wheel  may,  as  in  the 
above  example,  be  replaced  by  a  propelment  wheel,  such  that 
each  motion  of  the  armature  causes  it  to  move  on  one  tooth. 
The  latter  is  the  plan  now  most  in  use. 

The  right  number  of  currents  is  sent  by  means  of  a  dial 
at  the  sending  station,  and  an  index  with  a  handle  which 
can  be  turned  from  letter  to  letter;  the  letters  on  the  send- 
ing dial  correspond  in  number  and  arrangement  to  those  on 
the  receiving  dial.  The  handle  always  moves  in  one  direction 
and  sends  one  current  (positive  and  negative  alternately)  as  it 
passes  each  letter.  When  the  index  of  the  receiving  instrument 
and  the  handle  of  the  sending  instrument  have  once  been  set 
opposite  the  same  letter,  the  sending  operator  has  merely  to 
turn  his  handle  at  a  moderate  speed  to  each  letter  in  succes- 
sion which  he  wishes  to  send,  and  by  so  doing  he  will  send 
just  the  number  of  currents  required  to  bring  the  receiving 
index  step  by  step  to  the  same  letter.  Should  any  current 
or  currents  fail  to  move  the  receiving  index,  the  sender  and 
receiver,  finding  that  the  signals  are  not  understood,  put 
their  instruments  to  one  letter  or  mark  (sending  no  currents) 
by  a  mechanical  arrangement  contrived  for  the  purpose,  and 
recommence  the  message  from  the  point  at  which  it 
became  unintelligible.  The  currents  sent  by  the  handle  as 
it  is  turned  round  may  come  from  a  battery,  or,  as  is  more 
commonly  the  case,  from  a  magneto-electric  arrangement. 
Fig.  157  shows  the  magneto  transmitter  used  by  Messrs. 
Siemens. 

The  handle  H  is  fastened  to  the  spindle  A  carrying  the 
toothed  wheel  L,  which  latter  gears  into  the  pinion  T  of  the 
cylindrical  armature  or  keeper  E.  This  armature  E  is  mount- 
ed vertically  upon  pivots  between  the  poles  of  a  series  of 
permanent  magnets  G  G  G.  One  revolution  of  the  wheel  L, 
or  of  the  handle  H  fixed  thereto,  causes  the  pinion  of  the  arma- 
ture E  to  revolve  thirteen  times,  as  the  teeth  of  the  former 
are  in  the  proportion  of  thirteen  to  one  of  the  latter.  As  one 
full  turn  of  the  armature  produces  two  currents  of  opposite 


322 


Electricity  and  Magnetism.     [CHAP.  XXII. 


directions  in  a  coil  of  insulated  wire  forming  part  of  the 
cylindrical  armature  E,  twenty-six  currents,  alternately  posi- 
tive and  negative,  are  generated  during  one  revolution  of 
the  handle ;  the  dial  is  divided,  as  above  stated,  into 
twenty-six  parts,  viz.  twenty-five  letters  of  the  alphabet  (I 
,ind  J  being  taken  as  one)  and  one  blank. 


Sir  Charles  Wheatstone's  magneto-electric  letter-showing 
dial  step-by-step  instrument  is  perhaps  the  best  yet  intro- 
duced. 

When  a  radial  arm  is  employed  to  drive  the  armatures 
of  magneto-electric  induction  coils,  the  induced  currents 
are  generally  very  unequal  in  strength,  because  the  operator 
naturally  begins  and  ends  the  motion  comparatively  slowly. 
Sir  Charles  Wheatstone,  therefore,  drives  the  magneto- 
electric  armatures  continuously,  and  regulates  the  number  of 
currents  admitted  into  the  line  by  a  series  of  stops,  corre- 
sponding to  thirty  letters  and  symbols  arranged  round  a  dial. 
The  propelment  in  the  receiving  instrument  is  admirably 
light  and  accurate,  and  its  workmanship  very  perfect.  These 
little  instruments  are  chiefly  used  for  short  private  lines,  but 
have  been  employed  on  circuits  of  more  than  100  miles  in 
length. 


CHAP.  XXII.]        Telegraphic  Apparatus.  323 

§  14.  The  '  step  by  step '  printing  instrument  is  made  on  a 
plan  differing  little  from  that  of  the  letter- showing  instru- 
ment. The  pointer  is  replaced  by  a  ring  on  which  the  types 
of  the  required  letters  and  symbols  are  placed ;  this  ring  is 
turned  by  the  propelment  or  by  an  escapement  and  clockwork, 
so  that  each  required  letter  is  brought  in  turn  opposite  the 
paper  on  which  the  symbol  is  to  be  impressed  ;  the  paper  is 
then  struck  against  the  letter  on  the  ring  by  some  special 
device  differing  in  different  instruments.  In  one  the  mere 
pause  of  the  dial  suffices  to  allow  the  striking  or  printing 
hammer  to  act.  In  another  positive  currents  alone  are  used  to 
work  the  escapement,  and  a  negative  current,  sent  when  the 
desired  letter  is  reached,  determines  the  impression  by  the 
stroke  of  a  hammer.  In  a  third  a  second  line  wire  is  used 
to  give  the  blow  which  prints  the  letter.  The  paper  then 
moves  on  one  step.  These  instruments  have  not  come 
largely  into  use.  It  will  be  observed  that  the  number  of 
alternating  currents  required  for  each  letter  in  the  '  step  by 
step '  instruments  greatly  exceeds  the  number  required  by  in- 
struments of  Class  I. 

§  15.  The  Hughes  printing  instrument  is  the  typical 
synchronous  printer.  The  principle  on  which  it  is  based  may 
be  stated  as  follows  : — Two  type- wheels,  having  letters  on  their 
periphery,  one  at  the  sending  and  one  at  the  receiving  sta- 
tion, revolve  with  equal  velocity,  and  are  moreover  so  placed 
that  the  same  letter  in  each  wheel  passes  corresponding  fidu- 
cial marks  at  the  same  time.  The  fiducial  mark  in  the  receiv- 
ing instrument  is  opposite  a  little  roller,  carrying  a  strip 
of  paper  which  is  struck  against  the  edge  of  the  rotating 
wheel  by  the  release  of  the  armature  of  an  electro-magnet 
whenever  a  current  is  received  ;  a  letter  is  printed  by 
the  blow  without  stopping  or  sensibly  retarding  the  wheel ; 
the  paper  is  then  pulled  on  a  step  by  clockwork,  the  arma- 
ture replaced  on  the  electro-magnet,  and  all  is  in  readiness 
for  the  next  letter.  The  letter  which  is  printed 
depends  on  the  letter  of  the  wheel  which  happens  to  be 

Y  2 


3  2.4  Electricity  and  Magnetism.      [CHAP.  XXII. 

opposite  the  roller  and  paper  at  the  moment  when  the 
current  arrives.  A  series  of  keys  like  the  keys  of  a  piano- 
forte, and  each  lettered  to  correspond  with  the  letters  of  the 
alphabet,  are  so  arranged  relatively  to  the  sending  wheel  that 
the  depression  of  the  key  A  causes  a  single  current  to  be 
sent  when  A  is  opposite  the  fiducial  mark  at  the  sending 
station  ;  the  current  occupies  no  sensible  time  in  reaching 
the  other  station,  and  strikes  up  the  paper  when  the  A  on 
the  receiving  wheel  is  at  the  fiducial  mark.  The  letter  A  is 
therefore  printed  ;  if  the  operator  next  touches  the  key  N, 
the  sending  wheel  causes  a  current  to  pass  when  N  is  opposite 
the  fiducial  mark ;  at  the  same  instant  N  is  opposite  the 
paper  and  roller  at  the  receiving  station,  and  the  letter  N  is 
accordingly  printed.  This  action  can  be  repeated  inde- 
finitely with  any  series  of  letters  so  long  as  the  two  wheels 
keep  perfect  time.  Each  wheel  is  driven  by  clockwork, 
and  regulated  so  as  to  keep  very  nearly  perfect  time,  by  a. 
spring  pendulum,  which  vibrates  with  extreme  rapidity,  and 
regulates  a  frictional  governor  connected  with  each  wheel ; 
any  trifling  deviation  from  perfect  synchronism  is  corrected 
by  every  current  sent.  The  act  of  printing  slightly  accele- 
rates the  receiving  wheel  if  it  is  behind  time,  and  slightly 
retards  it  if  it  is  too  fast.  This  is  done  by  a  little  wedge 
which,  whenever  a  letter  is  printed,  is  forced  between  the 
teeth  of  a  star  wheel  fixed  to  the  type  wheel.  This  wheel 
is  not  rigidly  connected  with  the  axis  on  which  it  is  centred 
but  is  maintained  in  its  position  by  friction.  This  position 
can  therefore  be  corrected  without  sensibly  affecting  the 
speed  of  the  clockwork.  This  instrument  is  the  best  of  the 
printing  instruments  hitherto  introduced  :  it  has  the  great 
advantage  that  only  one  current  is  required  for  each 
letter. 

§  16.  Bakewell's  and  Caselli's  copying  telegraph  appara- 
tus requires  synchronous  motion  at  the  two  ends  of  the  line. 
The  principle  on  which  their  instruments  are  constructed 
may  be  explained  as  follows. 


CHAP.  XXII.]         Telegraphic  Apparatus.  325 

The  message  is  plainly  written  in  common  ink  on  a  sheet 
of  paper,  A,  covered  with  thin  tin  foil,  Fig.  158.  A  corre- 
sponding sheet  of  paper,  B,  is  chemically  prepared,  so  that 

FIG.  158. 
I/ 


when  a  current  passes  through  it  from  a  pointer  R  to  earth,  a 
mark  is  made  similar  to  that  used  in  Bain's  instrument.  The 
pointers  s  and  R  are  drawn  across  the  papers  A  and  B  in  a 
succession  of  parallel  equidistant  lines  with  a  perfectly  syn- 
chronous motion.  A  battery  is  connected  with  the  tinned 
paper,  the  line  L,  and  the  earth,  as  shown  in  the  sketch. 
When  the  pointer  s  touches  the  tin,  the  battery  is  short- 
circuited  through  the  tin;  no  sensible  current  reaches  B, 
and  R  leaves  no  mark ;  but  when  s  crosses  the  ink  on  A  the 
current  from  c  z  flows  through  L,  and  so  long  as  s  remains 
insulated  from  A  by  the  ink  a  line  is  drawn  by  the  point  R. 

It  is  easy  to  perceive  that  the  result  must  be 

-   .          .  .     ,       .  .  FIG.  159. 

as  accurate   a  copy  of  the  original  writing  as 

can  be  produced  by  a  series  of  fine  lines  inter- 
rupted in  the  proper  places,  as  in  Fig.  159. 

The  synchronism  required  is  in  Caselli's 
instrument  obtained  by  a  pendulum  at  each  re- 
ceiving station;  one  beat  of  the  pendulum  corresponds  to  each 
line  drawn  across  the  paper ;  the  one  pendulum  controls  the 
other  by  a  current  which  it  transmits  from  the  sending 
station  through  a  special  circuit  temporarily  connected  with 
the  line. 

§  17.  By  various  differential  arrangements  messages  can 
be  sent  simultaneously  in  both  directions  through  one  line. 
The  currents  sent  f:om  the  two  stations  do  not  really  travel 


326 


Electricity  and  Magnetism.      [CHAP.  XX I  r. 


simultaneously  in  opposite  directions  through  the -line,  but 
the  effect  of  the  signals  on  each  receiving  instrument  is 
precisely  the  same  as  thcugh  the  line  were  being  worked  in 
only  one  direction. 

Let  the  connections  be  arranged  as  in  Fig.  160.  R  and  r 
represent  two  relays,  each  wound  with  two  coils  capable  of 
producing  equal  magnetization  in  the  core  if  equal  currents 
are  passed  through  both  coils.  If  equal  currents  pass  in 
opposite  directions  through  the  two  coils,  the  coil  will  neither 
be  magnetized  nor  demagnetized.  M  and  m  are  two  Morse 
keys,  so  made  that  the  line  must  always  be  in  contact  with 
the  earth  or  the  battery,  or  (for  a  very  short  time,  as  the  key 
moves)  with  both.  When  the  handle  at  M  is  untouched, 
there  is  unbroken  connection  from  the  line  round  the  inner 
coil  of  the  relay  to  earth  through  the  contact  o  and  the  wire 
v.  There  is  a  second  connection  between  the  line  and  the 
earth  from  the  point  N,  through  the  outer  coil  of  the  relay, 
and  through  the  resistance  coils  w.  The  condenser  D  is 
connected,  as  shown,  with  this  branch. 

When  the  handle  M  is  depressed,  contact  is  made  at  P, 

FIG.  160. 


which  for  an  instant  short-circuits  the  battery  c  z  through 
the  wires  vt  and  v,  and  immediately  afterwards  contact  is 
broken  at  o,  so  that  the  battery  c  z  is  connected  with  w  and 
thence  with  two  circuits,  one  through  the  line  to  the  distant 


CHAP.  XXII.]          Telegraphic  Apparatus.  327 

station  and  one  through  the  outer  branch  of  the  relay  to 
earth  at  the  Home  station  through  w. 

The  resistance  of  w  is  made  equal  to  that  of  the  line  L, 
added  to  that  part  of  the  circuit  by  which  L  is  connected  with 
earth  at  the  distant  station ;  the  capacity  of  D  is  so  chosen 
that  w  and  D  may  represent  an  artificial  line  in  all  respects 
equivalent  to  the  real  line. 

Thus  there  may  be  nine  arrangements  of  the  positions  of 
the  keys  M  and  m. 

1.  Let  M  be   depressed  and  m  untouched.     The  battery 
c  z  sends  a  current  round  both  coils  of  R,  which  does  not 
work,  as  the  currents  flow  in  opposite  directions;  it  also  sends 
a  current  through  the  line  L,  and   thence  round  the  inner 
coil  of  r  and  to  earth  through  o ;  the  relay  r  works  and 
gives  a  signal. 

2.  Let  M   be   depressed  and    m  also    depressed.     The 
currents  which  each  battery  would  send   through  the  line 
neutralise  one  another,  but  each  battery  sends  a  current 
through  the  outer  coil  of  its  own  relay ;  both  relays  work, 
and  signals  are  received  at  both  stations.     The  current  sent 
through  the  outer  coil  of  each  relay  is  equal  to  that  which 
the  battery  would  send  through  the  line  and  inner  coil  of 
the  distant  relay. 

3.  Let  m  be  depressed  and  M  untouched.     This  case  is 
similar  to   the    first  case;    a   signal   is   indicated  by  the 
relay  R. 

4.  Let  neither  key  be  depressed,  both  batteries  are  cut 
off  the  line  and  no  signal  is  indicated  by  either  relay. 

5.  Let  both  M  and  m  be  in  the  intermediate  position, 
contact  made  at  p  and  p  but  not  broken  at  o  or  o.     No 
signal  will  be  given  at  either  station. 

6  and  7.  Let  the  key  at  M  or  m  be  in  the  intermediate 
position  and  the  other  key  not  depressed ;  no  signal  will 
be  indicated  at  either  station. 

8.  Let  the  key  at  M  be  in  the  intermediate  position  when 
m  is  depressed,  the  current  produced  by  c  z  will  be  un- 


328  Electricity  and  Magnetism.      [CHAP.  XXII. 

altered,  and  the  signal  will  be  received  through  the  inner 
coil  of  R. 

9.  If  the  key  at  m  is  in  the  intermediate  position,  and  M 
depressed,  a  signal  will  be  received  by  the  inner  coil  of  r. 

In  every  arrangement  of  the  keys  M  and  m,  the  effect  pro- 
duced on  the  relays  is  such  that  when  m  is  depressed  R 
receives  a  signal,  when  M  is  depressed  r  receives  a  signal. 

This  arrangement  is  a  modification  of  that  introduced  by 
Messrs.  Siemens  and  Frischen,  and  is  due  to  an  American, 
Mr.  Stearns. 

Mr.  Stearns  finds  it  advantageous  to  introduce  two  resist- 
ance coils,  v  and  vt  ;  v  is  made  equal  to  v^  +  the  battery 
resistance;  and  vl  is  chosen  sufficiently  large  to  prevent 
the  polarization  of  the  battery  when  momentarily  short- 
circuited  through  v  and  v^ 

By  short-circuiting  the  battery,  Mr.  Stearns  is  able  to  avoid 
insulating  the  point  N  when  the  key  M  is  in  its  intermediate 
position.  If  N  were  insulated,  the  received  current  would 
pass  round  both  coils  of  the  relay  and  would  pass  to  earth 
through  the  resistance  w.  At  first  sight  this  latter  arrangement 
(which  was  that  used  by  Messrs.  Siemens  and  Frischen) 
seems  perfect,  for  we  have  the  current  diminished  to  one- 
half  by  a  doubled  resistance  and  at  the  same  time  acting 
with  double  force  per  unit  of  current  on  the  relay.  This 
reasoning  does  not  take  into  account  the  inductive  retarda- 
tion (Chap.  XXIII.)  produced  by  artificially  lengthening  the 
line.  Mr.  Stearns,  in  all  positions  of  the  key,  signals  through 
a  line  of  constant  length  and  capacity. 

BELLS. 

§  18.  Bells  may  be  classed  as  a  distinct  kind  of  tele- 
graphic apparatus.  Besides  the  bells  which  have  already 
been  described,  in  which  each  signal  sent  causes  the  hammer 
to  strike  one  blow,  there  are  two  kinds  of  electric  bells  : — 
First,  those  in  which  the  hammer  is  driven  by  a  weight  and 
clockwork ;  the  clockwork  remains  at  rest  so  long  as  a  certain 


CHAP.  XXIII. ]         Speed  of  Signalling.  329 

detent  or  trigger  restrains  it,  but  runs  down,  striking  the 
bell,  so  long  as  the  detent  is  held  back  by  the  armature  of  an 
electro-magnet  actuated  by  the  received  current.  While  the 
current  is  maintained,  the  weight  runs  down  and  the  bell 
continues  to  ring.  Secondly,  those  in  which  the  hammer  is 
attached  to  the  armature  of  the  electro-magnet,  and  is  fur- 
nished with  contact  pieces  (as  in  RuhmkofFs  coil),  such  that 
when  the  armature  is  attracted  to  strike  a  blow,  the  contact 
is  broken,  and  the  current  ceasing,  the  armature  returns  to 
its  original  place,  makes  contact  again,  and  is  again  impelled 
to  strike  a  blow.  This  action  is  repeated  so  long  as  a  cur- 
rent is  sent  from  the  sending-station.  The  second  form  of 
bell,  sometimes  called  a  trembler,  is  the  more  convenient,  and 
is  used  for  household  and  hotel  purposes. 

Electric  bells  may  with  especial  propriety  be  introduced 
.into  hospitals,  and  may  be  employed  even  in  private  houses 
by  invalids.  The  effort  required  to  ring  the  electric  bell  is 
that  of  making  contact  at  one  part  of  the  circuit.  This  can 
be  done  by  the  smallest  pressure  on  the  little  button  of  a 
handle  or  little  box,  which  can  be  held  in  the  hand  in  bed, 
and  attached  by  flexible  wires  to  the  wall.  This  arrange- 
ment allows  the  patient  to  assume  any  posture  without 
losing  command  of  the  bell.  Electric  bells  are  also  used 
for  railway  signalling,  and  in  all  telegraph  stations  to  call  the 
attention  of  the  clerks. 


CHAPTER  XXIII. 

SPEED    OF    SIGNALLING. 


§  1.  ELECTRICITY  cannot  properly  be  said  to  have  a  velocity. 
It  is  true  that  when  a  circuit  is  completed  at  any  one  point, 
electrical  effects  are  not  produced  at  other  points  of  the 
circuit  until  a  sensible  time  has  elapsed ;  so  that,  for  instance, 
when  a  signal  is  sent  through  the  Atlantic  cable,  it  does  not 


33°          .        Electricity  and  Magnetism.     [CHAP.  xxin. 

produce  any  effect  in  Newfoundland  simultaneously  with  the 
depression  of  the  key  in  Ireland.  The  distance  divided  by 
the  time  occupied  in  the  transmission  of  the  signal  may  be 
called  the  velocity  with  which  that  particular  signal  was 
transmitted  ;  it  might  even  be  termed  the  velocity  with 
which  a  certain  quantity  of  electricity  traversed  the  cable, 
but  it  is  not  the  velocity  proper  to  or  peculiar  to  electricity, 
for  under  different  circumstances  the  same  quantity  of  elec- 
tricity may  be  made  to  traverse  the  same  distance  with 
almost  infinitely  different  velocities. 

.  For  about  two-tenths  of  a  second  after  contact  is  made  in 
England,  no  effect  can  be  detected  in  Newfoundland  even 
by  the  most  delicate  instrument :  after  "4"  the  received  current 
is  about  7  per  cent,  of  the  maximum  permanent  current 
which  will  ultimately  flow  equally  through  all  parts  of  the 
circuit.  The  current  will  gradually  increase  until,  i"  after 
the  first  contact  was  made,  the  current  will  have  reached 
about  half  its  final  strength,  and  after  about  3"  it  will 
have  attained  nearly  its  maximum  strength ;  during  the 
whole  time  the  maximum  current  is  flowing  into  the  cable  at 
the  sending  end.  The  velocity  with  which  the  current 
travels  even  in  this  one  case  has  therefore  no  definite  mean- 
ing  ;  the  current  does  not  arrive  all  at  once  like  a  bullet,  but 
grows  gradually  from  a  minimum  to  a  maximum.  The 
time  required  for  any  given  similar  electrical  operation  on 
various  lines  is  directly  proportional  to  the  capacity  of  the 
unit  of  length  of  the  conductor,  to  the  resistance  per  unit 
of  length,  and  to  the  square  of  the  length  intervening  between 
the  sending  and  receiving  station.  Fig.  161  shows  the  curve 
representing  the  law  of  increase  of  the  received  currents, 
which  is  the  same  on  all  lines.  The  vertical  ordinates  parallel 
to  o  Y  represent  strengths  of  current,  the  maximum  or  per- 
manent current  flowing  through  the  circuit  after  equilibrium 
has  been  reached  being  called  100. 

The  horizontal  ordinates  parallel  to  o  x  represent  intervals 
of  time,  measured  from  the  time  at  which  contact  was  first 


CHAP.  XX III.]          Speed  of  Sig  nailing. 


331 


made,  and  expressed  in  terms  of  an  arbitrary  unit,  a,  different 
for  different  circuits,  but  constant  for  any  one  circuit.  For  a 
uniform  line  of  the  length  /,  the  resistance  per  unit  of  length 


FIG.  161. 


R  and  the  capacity  per  unit  of  length  s,  the  value  of  a  is 
given  in  seconds  by  the  expression 

a  =  S-^/-  log,  (10*)  =  -02332  S  R  /2 1°. 

In  this  expression  absolute  measure  (gramme  metre  second) 
is  used.  When  Sj  is  measured  in  microfarads  per  knot,  R!  in 
ohms  per  knot,  and  /j  in  knots,  the  above  expression  becomes 
a  =  -02332  st  RJ  /j2  -7-  io6  .  .  .  .  2°. 

For  the  French  Atlantic  Cable  we  have  B!  =  0^43 
R!  =  2-93  and  /j  =  2584;  and  hence  for  a  the  value  -196 
second. 

In  terms  of  a  the  arrival  curves  for  the  received  current  of 
all  lines  are  identical,  and  the  same  curve  shows  the  law 

FIG.  162. 


according  to  which  the  current  at  the  receiving  end  dies 
away  when  at  the  sending  end  the  line  has  been  put  to 
earth.  A  succession  of  contacts  with  a  battery  and  with 
earth  at  the  sending  end  prolonged  each  for  times  equal 
to  about  25  a  would  produce  the  series  of  changes  in  the 


332 


Electricity  and  Magnetism.     [CHAP.  XXIII. 


received  current  shown  in  Fig.  162,  each  curve  being  a  com- 
plete arrival  curve. 


FIG.  i62A. 


The  annexed  table  shows  the  value  of  the  vertical  ordi- 
nates  corresponding  to  successive  multiples  of  o,  the  maximum 
current  being  100. 


*in 
terms 
of  a 

Strength  of 
current  in  per- 
centages. 

/  in 
terms 
of  a 

Strength 
of  current 
in   per- 
centages. 

t  in 
terms 
of  a 

Strength 
of  current 
in  per- 
centages. 

/  in 
terms 
of  a 

Strength 
of  current 
in  per- 
centages. 

'4 

•OOOOOOOO27I 

I'l 

•04140636 

3'5 

18-48434 

7-8 

66-95995 

•5 

•00000051452 

1-2 

•08927585 

3-6 

19-84366 

8-0 

68-42832 

•55 

•0000033639. 

I'3 

•1704802 

37 

2I-2I342 

8-5 

71-82887 

•60 

•000016714 

I'4 

•2959955 

3-8 

22-59017 

9-0 

74-87I72 

•62 
•64 

•000029252 
•000049412 

i  '5 

1-6 

•476336 
720788 

3'9 
4-o 

23-97071 

25'352I7 

9'5 
10-0 

77-59133 
80-02000 

•66 

•000080817 

1-7 

I  '036905 

4-2 

28-10757 

10-5 

82-18760 

•68 

•00012835 

1-8 

1  -430252 

4'4 

30-83807 

n-o 

84-12139 

70 

•00019845 

1-9 

I  -904356 

4-6 

33-52902 

12 

87-38402 

72 

•00029937 

2'O 

2-460812 

4-8 

36-16892 

13 

89-97752 

74 

•00044152 

2'I 

3-09969 

5-o 

38-74814 

H 

92-03836 

76 

•00063776 

2'2 

3-81846 

5'2 

41  -26032 

15 

93^7565 

•78 

•00090371 

2-3 

4-61560 

5'4 

43-70028 

16 

94-97631 

•80 

•00125804 

2"4 

5-48661 

5-6 

46  -06449 

17 

96-00951 

•82 

•00172272 

2'5 

6-42695 

5-8 

4835o7o 

18 

96-83023 

•84 

•00232333    . 

2'6 

7-43I63 

6-0 

50-55770 

19 

97-48215 

•86 

•00308919 

27 

8-49536 

6-2 

52-68501 

20 

98  -ooooo 

•88 

•00405358 

2-8 

9-61264 

6-4 

54-733I4 

21 

98-41134 

•90 

•00525387 

2'9 

10-77797 

6-6 

56-70294 

22 

9873809 

•92 

•00673158 

3-0 

11-98582 

6-8 

58-9502 

23 

98-99763 

•94. 

•00853247 

3'I 

13-23087 

7-0 

60-41164 

24 

99-20379 

•96 

•01070646 

3-2 

14-50800 

7-2 

62-15439 

25 

99-36754 

•98 

•01330764 

3'3 

I5-8I233 

7'4 

63-82523 

I  -00 

•01639420 

3'4 

I7-I392I 

7-6 

55-42636 

j 

CHAP.  XXIII.]          Speed  of  Signalling. 


333 


When  the  line  is  put  to  earth  at  the  sending  end  before 
the  maximum  current  is  reached,  the  falling  curve  is  super- 
imposed on  the  ascending  one,  and  a  derived  curve  is  pro- 
duced as  shown  in  Fig.  162  A,  which  gives  the  effect  of  mak- 
ing contact  for  5  a  and  then  putting  the  line  to  earth.  At 
the  time  6  a  from  the  beginning  of  the  operations  the 
strength  of  current  will  be  50*55770  —  '01639  =  50-54131; 
and  at  the  end  of  7  a  it  will  be  60-41164  —  2-46081  = 
57-95083  ;  and  in  this  manner  the  whole  of  the  derived  curve 
can  be  traced.  If  now  the  line  be  put  in  contact  with  the 
battery  again  at  the  end  of  7  a,  the  third  curve  can  be 
derived  by  again  superimposing  the  original  curve  on  the 
first  derived  curve  ;  so  that  at  the  end  of  8  o  the  strength 
would  be  68-42832  —  11-98582  +  '01639420;  and  in  this 
manner  the  effect  of  any  number  of  operations  can  be  com- 
puted. 

§  2.  It  follows  from  the  above,  that  the  result  of  a  series 
of  short  equal  contacts  alternately  with  earth  and  a  battery  at 
the  sending  end  will  produce  a  small  series  of  rises  and  falls 
in  the  strength  of  the  current,  which  grow  smaller  and 
smaller  as  the  length  of  the  contacts  diminishes  :  the  mean 
strength  of  the  current  will  be  half  the  permanent  maximum 
produced  by  a  permanent  current ;  and  when  the  alternate 
contacts  are  made  short  compared  with  o,  no  sensible 
variation  can  be  detected  in  the  current  which  flows  from  the 
cable  at  the  receiving  end.  As  the  contacts  are  lengthened, 
the  amplitude  of  variation  increases.  The  following  table 
gives  some  amplitudes  due  to  a  succession  of  simple  dots  or 
equal  contacts  with  the  earth  and  with  a  battery. 


Length  of  pair  of  contacts  \    . 
in  terms  of  a.     .  .  J     ' 


Amplitude  of  variation    of] 
current     in    percentages  r  z'6g 
of  maximum.     .     .     .     .} 


2-97 


3 '5 


6-31 


7-0 


9'o    10 


19*67  24 '42  29 'i i  33 '68 


The  theory  of  the  speed  of.  signalling  was  first  given  by 
Sir  William  Thomson,  read  before  the  R.  S.  May  24,  1855, 
published  in  the  Proceedings,  and  reprinted  in  the  Phil.  Mag., 
February  1856. 


334  Electricity  and  Magnetism.     [CHAP.  XXIIL 

§  3.  Signals  sent  through  land-lines  last  so  long  relatively 
to  the  exceedingly  short  value  of  a  for  such  lines,  that  in  all 
ordinary  cases  the  current  rises  almost  to  its  maximum,  and 
falls  to  zero  at  each  dot.  The  capacity  in  electrostatic 
measure  of  wire  of  diameter  d  suspended  at  a  height  h  above 
a  flat  plane,  and  remote  from  all  other  conductors,  is 


Taking  6=3  metres  and  </=  0*004  metre,  we  have  s  =  0*062, 

or  in  absolute  electro-magnetic  measure  s  =   -  -  —  TRT, 

(28-8  x  io9)2 

or  about  "013  microfarad  per  statute  mile.  There  is  ex- 
perimental reason  to  believe  that  the  actual  capacity  is 
about  double  this  amount,  or  even  a  little  more,  owing  to  the 
induction  between  the  wire  and  the  posts  and  insulating 
supports.  Even  taking  s  as  '03  microfarad,  and  the  resist- 
ance of  a  mile  of  '004  mm.  wire  as  15  ohms,  we  have  for 
a  line  350  miles  long 

a  =  '00126  second. 

This  value  is  so  small  that  even  with  20  a  for  each  con- 
tact and  40  a  for  each  dot,  the  dot  would  only  occupy 
•05",  or  20  dots  could  be  made  in  a  second  ;  and  for  every 
dot  the  current  would  rise  almost  to  its  maximum  and  fall 
almost  to  its  minimum.  The  above  speed  would  give  about 
80  words  per  minute  as  a  speed  at  which  the  effect  of  what 
is  called  retardation  would  be  insensible  in  diminishing  the 
rise  and  fall  of  the  received  current. 

Instruments  intended  for  use  upon  land-lines  are  therefore 
invariably  constructed  on  the  hypothesis  that  the  received 
current  will  at  each  signal  rise  and  fall  through  a  consider- 
able percentage  of  its  maximum  strength.  The  spring 
attached  to  the  armature  of  the  electro-magnet  is  adjusted 
so  that  at  some  one  strength  of  received  current  the 


CHAP.  XXIIL]          Speed  of  Signalling.  335 

armature  will  rise,  and  at  another  strength  differing  little 
from  the  former  it  will  fall  :  in  order  to  work  such  an 
instrument  safely,  the  received  current  must  rise  much  above 
the  first  and  fall  far  below  the  second  strength,  and  this  is 
the  case  even  when  100  words  per  minute  are  sent  by 
Professor  Wheatstone's  automatic  sender  from  London  to 
Edinburgh. 

§  4.  On  submarine  lines  any  such  condition  as  a  great 
and  regular  rise  and  fall  in  the  received  current  limits 
the  speed  of  transmission  very  seriously :  40  a  for  the 
French  Atlantic  cable  corresponds  to  nearly  8  seconds, 
and  two  minutes  would  be  required  for  the  transmission 
of  each  word,  if  this  interval  of  time  were  required  for  each 
dot;  whereas  from  15  to  17  words  have  actually  been  sent 
through  this  cable  in  a  minute.  The  duration  of  a  dot  at  the 
speed  of  15  words  per  minute  must  have  been  about  "27 
second,  or  about  i'38  a.  Many  of  the  dots  can  have  pro- 
duced no  more  variation  in  the  received  current  than  is 
equivalent  to  -nrVffth  of  the  permanent  current ;  the  theory  of 
superimposed  signals  shows  us  that  the  exact  effect  of  any  one 
positive  or  negative  dot  depends  on  the  20  or  30  preceding 
signals,  so  that  even  very  regular  sending  produces  irregular 
results  at  the  receiving  end.  Signals  such  as  these  cannot 
be  received  by  any  arrangement  of  armatures  or  other 
apparatus  which  moves  at  a  fixed  strength  of  current,  but  re- 
quire some  arrangement  which  shall  be  capable  of  following 
and  indicating  or  recording  every  change  in  strength  of 
the  received  current.  Sir  William  Thomson,  by  his  inven- 
tion of  the  mirror  galvanometer  so  constructed  that  it 
could  fulfil  this  condition,  rendered  submarine  telegraphy 
commercially  practicable.  The  spot  of  light  wanders  over 
the  scale,  following  every  change  of  current,  and  the  clerks  by 
degrees  acquire  sufficient  skill  to  interpret  the  seemingly 
irregular  motions.  One  dot  will  cause  the  light  almost  to 
cross  the  scale,  the  second  moves  it  a  little  farther,  the  third 
or  fourth  hardly  cause  a  perceptible  motion,  but  the  clerk 


336 


Electricity  and  Magnetism.    [CHAP.  ;XXIII. 


by  experience  knows  that  the  four  very  different  effects  each 
indicate  a  simple  dot,  each  sent  by  the  clerk  at  the  other  end 
in  a  precisely  similar  manner. 

§  £.  Sir  William  Thomson's  syphon  recorder  actually  draws 
on  paper  the  curves  which  we  have  learnt  to  construct  theo- 
retically. Ink  is  spurted  from  a  fine  glass  tube  on  to  paper 

FIG.  16^. 


drawn  past  it  with  a  uniform  motion  :  the  glass  point  of  this 
tube  moves  to  the  right  or  left  through  distances  proportional 
at  each  instant  to  the  strength  of  the  current,  and  thus  the 
signals  are  drawn  on  the  paper  in  the  form  of  curves  repre- 
senting the  strength  of  the  current  at  each  instant  of  time. 
The  glass  tube n  (Fig.  163)  is  pulled  backwards  and  forwards 


CHAP.  XX1IL]  Speed  of  Signalling. 


337 


by  being  connected  through  the  threads  k  h  and  lever  i  with 
a  very  light  movable  coil  b  b,  placed  between  the  two  poles 
of  a  very  powerful  electro -magnet,  not  shown. 

A  soft  iron  fixed  core  a  is  placed  in  the  centre  of  the 
coil.  The  coil  oscillates  about  a  vertical  axis,  being  directed 
by  a  bifilar  arrange m en t//i.  The  received  current  passes 
through  this  coil  from  the  terminals  /  /j  :  the  vertical  arms 
of  the  coil  are  impelled  across  the  magnetic  field  in  one 
direction  or  the  other  according  to  the  sign  and  strength  of 
the  received  current.  The  magnetic  field  in  this  arrange- 
ment is  very  intense  and  very  uniform,  which  gives  great 
sensibility  to  the  apparatus.  The  glass  syphon  //  is  strung 
on  the  wire  /  /„  the  shorter  end  dips  in  the  ink-trough  arc,  and 
the  longer  end  is  opposite  the  paper  o\  the  syphon  can  be 
withdrawn  from  the  ink  by  the  slide  p ;  the  spring  g  keeps 
the  threads  k  h  taut ;  the  directing  force  of  the  bifilar  ar- 
rangement is  adjusted  by  varying  the  position  of  the  bracket 
r ;  the  two  weights  w  w^  hang  from  the  coil  by  the  two 
directing  threads. 

If  the  coil  is  shunted  so  that  there  is  a  comparatively  short 
circuit  through  which  the  current  induced  by  its  motion  can 
flow,  the  electro-magnetic  induction  of  the  magnet  on  the 
coil  tends  to  check  rapid  oscillations  not  due  to  the  signals. 

FIG.  164. 


A  certain  portion  of  the  received  current  is  lost  through  the 
shunt,  which  is,  however,  rarely  required,  for  the  capacity  of 


338 


Electricity  and  Magnetism.     [CHAP.  XXIII. 


the  cables  connected  with  the  coil  is  such  that  a  very 
sensible  induction  takes  place  even  without  the  shunt. 

The  ink  is  electrified  by  an  induction  machine  similar  in 
principle  to  that  described  in  Chapter  XIX.  §  i,  and  is 
thus  made  to  fly  to  the  oppositely  electrified  strip  of  paper 
in  a  succession  of  fine  drops. 

§  6.  If  it  were  necessary  to  allow  the  recording  point  to 
travel  over  the  whole  possible  range  of  the  received  current, 
it  is  clear  that  practically  dots  of  only  y^^  of  the  maxi- 
mum strength  would  correspond  to  T^Vrr  °f  tne  breadth  of 
the  paper,  and  could  not  be  made  legible  with  any  practi- 
cable breadth  of  paper.  They  are  legible  on  the  mirror 
galvanometer  because  the  light  can  range  over  a  length  of 
some  feet,  but  J  inch  is  a  broad  paper  strip  for  any  re- 
cording instrument.  Mr.  Varley's  mode  of  signalling  by 
condensers  supplies  the  means  of  keeping  the  light  of  the 
mirror  galvanometer  always  at  one  part  of  the  scale,  and  the 
glass  tube  end  of  the  recorder  within  a  very  narrow  strip  of 
paper. 

The  line  L,  Fig.  164,  is  attached  to  the  insulated  armatures 

FIG.  165. 


d. 


m-     TL 


undcrstwzd 

N  and  n  of  two  large  condensers ;  the  second  armature  M  at 
the  sending  end  is  connected  to  a  key  K,  by  which  it  can  at 
will  be  connected  with  the  battery  c  z  or  with  earth  ;  the 
armature  m  is  permanently  connected  through  the  receiving 
instrument  R  with  earth. 

When  by  the  key  K,  M  is  connected  with  the  positive  pole, 
N  is  rendered  negative  by  induction ;  a  current  flows  from 
N  to  a ;  n  becomes  positive  and  m  negative  by  induction, 


CHAP.  XXIII.]  Speed  of  Signalling.  339 

and  to  charge  m  negatively,  a  short  current  flows  from  m  to 
E  through  R,  making  the  desired  signal  in  one  direction  ; 
the  current  sent  through  R  begins  suddenly,  is  very  small, 
and  would  gradually  die  out,  even  if  M  were  not  put  to 
earth:  the  fall  in  the  current  is,  however,  accelerated  by 
raising  the  key  and  putting  M  to  earth.  A  negative  signal 
is  given  by  connecting  M  with  the  zinc  instead  of  the 
copper  pole  of  the  battery. 

With  this  arrangement  no  electricity  flows  into  or  out  of 
the  cable  but  by  induction  :  the  charge  in  the  cable  is  re- 
arranged at  each  signal.  The  current  received  through  the 
instrument  R  never  increases  beyond  that  due  to  the  first 
signal. 

Fig.  165  shows  the  alphabet,  and  Fig.  166  shows  a 
message  sent  with  condensers  and  received  by  the  recorder. 

FIG.  166. 


I/  e  <?    was    t  a.  p  p    i  n  <? 

Mr.  Varley's  system  has  the  additional  advantage  that  no 
permanent  earth  currents  can  flow  through  the  line,  for  the 
line  is  not  connected  anywhere  with  earth.  A  sudden  change 
of  potential  in  the  earth  at  either  end  will  induce  a  current, 
but  sudden  changes  are  much  rarer  than  slow  changes,  and 
the  latter,  however  great,  are  quite  cut  off  by  the  condensers. 

§  7.  The  time  of  every  electrical  operation  is  proportional 
to  a,  or  to  s  R  /2  ;  and  consequently,  whatever  instrument  is 
employed  to  record  or  receive  the  messages,  the  speed  of 
working  must  with  that  instrument  be  inversely  proportional 
to  s  R  /*,  and  with  any  cables  of  uniform  construction  the 
speed  must  be  inversely  proportional  to  the  square  of  the 
length. 

The  speed  will,  however,  differ  enormously,  according  to 
the  nature  of  the  electrical  operation  required  for  working 

z  2 


34O  Electricity  and  Magnetism.    [CHAP.  XXIV. 

the  instrument.  Thus  the  Morse  instrument  probably  requires 
that  the  dots  should  occupy  a  time  of  from  15  to  20  a,  and  is 
therefore  about  14  times  slower  than  the  mirror  galvanometer, 
which  will  show  dots  of  i  or  1*2  a.  The  speed  of  the 
syphon  recorder  is  nearly  equal  to  that  of  the  mirror. 

The  speed  depends  on  the  weight  per  knot  w  of  the  copper 
and  on  the  weight  per  knot  w  of  the  gutta  percha  employed, 
and  may  be  calculated  from  the  following  formula,  where  L 
is  the  length  of  the  cable  in  knots. 

Speed  by  mirror  in  words  per  minute — 

log  (70-4  w  +  480  w)  —  log  64  w 

=  0-2325  W  —  — a- L ° X    I06 

If  Mr.  Willoughby  Smith's  material  is  used  instead  of  gutta 
percha,  the  multiplier  -275  may  be  used  instead  of  0*2325  ; 
and  for  Hooper's  material,  if  the  specific  gravity  is  such  that 

D2  —  d* 

its  weight  per  knot  is ^—  Ibs.,  and  its  specific  induc- 
tive capacity  3*3,  the  above  formula  becomes 

^  log  (7o'4.g/  +  400  w)  -  log  64  w  x  IQ6 

L 

The  speeds  given  correspond  to  13  words  per  minute 
through  the  French  Atlantic  Cable.  As  many  as  17  have 
occasionally  been  sent.  For  Morse  instruments  the  above 
speeds  must  be  divided  by  14. 

It  will  be  observed  that  when  a  constant  ratio  is  main- 
tained between  the  weights  per  knot  of  dielectric  and  con- 
ductor, the  speeds  of  working  are  directly  proportional  to 
the  quantities  of  material  used. 


CHAPTER  XXIV. 

TELEGRAPHIC   LINES. 


§  1.  A  TELEGRAPHIC  line  is  an  insulated  wire  reaching  from 
station  to  station.  On  land  an  iron  wire  is  generally  used, 
supported  on  stoneware,  porcelain,  glass,  or  vulcanite  insula- 


CHAP.  XXIV.]  Telegraphic  Lines.  341 

tors  carried  by  wooden  or  iron  posts.  Sometimes  underground 
wires  are  used,  and  these  are  generally  made  of  copper  insu- 
lated with  gutta  percha  or  india  rubber,  and  protected  by 
tape,  leaden  or  iron  tubes,  wooden  troughs  rilled  with 
bitumen,  or  an  iron  wire  serving.  Submarine  lines  invaria- 
bly have  a  copper  conductor  insulated  with  gutta  percha  or 
some  preparation  of  india  rubber,  forming  what  is  called  a 
core.  This  core  is  served  with  hemp  or  jute,  and  covered 
helically  with  iron  or  steel  wires,  which  are  further  covered 
in  many  cases  with  hemp  and  tar,  or  a  bituminous  compound. 
It  is  desirable  that  the  conductor  of  a  telegraphic  line  should 
have  a  small  resistance,  and  that  it  should  be  well  insulated. 
The  smaller  the  resistance  of  the  line,  the  smaller  .the 
battery  required  to  work  it,  and  with  a  given  insulation  the 
smaller  the  leakage.  On  submarine  lines  the  speed  attain- 
able is  increased  by  diminishing  the  resistance  of  the  con- 
ductor. Bad  insulation  or  great  leakage  involves  the  use  of 
large  batteries,  frequent  adjustment  of  the  receiving  instru- 
ments to  suit  variations  in  the  received  currents,  resulting 
from  variation  in  the  resistance ;  bad  insulation  also  involves 
greatly  increased  difficulty  in  ascertaining  by  electrical  tests 
the  position  of  any  injury  occurring  to  the  line.  The  follow- 
ing paragraphs  relate  chiefly  to  the  modes  practically  adopted 
for  securing  moderate  resistance  and  high  insulation  : 

§  2.  The  iron  wire  used  in  land  lines  is  in  this  country 
generally  No.  8,  B.W.G.  £  inch  diameter. 

The  following  table  (p.  340)  gives  some  of  the  other  sizes 
adopted.  The  weights  per  statute  mile  are  taken  from 
Mr.  Clark's  tables.  There  are  considerable  differences  in 
the  weights  given  by  different  authors,  and  I  am  not  aware 
that  any  one  set  of  tables  are  authoritative. 

Mr.  Culley  gives  No.  8  wire  as  0-17  inches  diameter;  its 
resistance  13*5  ohms,  and  that  of  No.  4  as  y8  ohms.  There 
is  great  difference  in  different  specimens.  The  strength  of 
good  iron  wire  varies  from  20  tons  per  square  inch  for  large 
gauges  such  as  No.  i  to  40  tons  per  square  inch  for  No.  8 


342 


Electricity  and  Magnetism.    [CHAP.  XXIV. 


and  smaller  sizes.  Mr.  Culley  gives  1,300  Ibs.  for  No.  8,  and 
this  corresponds  by  the  above  table  to  367  tons  per  square 


Resist- 
ance in 

Strain 

Size  of  wire, 

B.W.G. 

Dia- 

meter  in 
inches. 

.  Weight 
in  cwts. 
per 
statute 

ohms 
at  ordi- 
nary tem- 
peratures 

corre- 
sponding 
to  10 
tons  per 

Where  used. 

mile. 

per 

inch 

statute 
mile. 

(cwt.) 

I 

2 

•284 

1245 
III7 

4'i6 

4'57 

I4'I3 
12-66 

\  India.     Some  long 
\  lines  in  England. 

4 

•238 

783 

6-51 

8-89 

6 

•203 

570 

8-96 

6-47 

Germany 

8 

•I65 

376 

13-6 

4-27 

England  and  Germany 

10 

•134 

249 

20-5 

2-82 

England,  short  lines 

4  millimetres 

•157 

340 

15*0 

3-86 

France 

3  millimetres 

•118 

I92 

267 

2-18 

" 

inch.  The  iron  wire  should  be  galvanized,  and  should  be 
capable  of  being  bent  round  itself  and  unbent  without 
injury.  It  should  also  stand  bending  four  times,  first  one  way 
and  then  the  other,  to  a  right  angle,  being  held  in  a  vice. 
The  wire  is  stretched  2  per  cent,  cold  before  being  used. 
This  process  is  called  killing,  and  not  only  detects  weak 
places,  but  makes  the  wire  less  springy  and  more  manageable. 
It  should  be  painted  or  varnished  in  smoky  places. 

From  25  to  20  poles  per  mile  may  be  used  on  straight 
lines,  but  16  poles  per  mile  are  sometimes  used  if  no  more 
than  four  wires  are  required.  On  sharp  curves  as  many  as  40 
poles  per  mile  may  be  required.  The  fewer  the  poles  the  better 
the  insulation.  For  10  wires  or  less  the  diameter  of  wooden 
poles  may  be  5  inches  at  the  top ;  for  a  larger  number  of 
wires  6  inches.  Creosoted  larch  is  the  best  material  ;  and 
the  batts  should  be  charred  and  baked  to  prevent  decay, 
and  tarred  if  well-seasoned.  The  pole  above  ground  should 
be  painted. 

The  distance  between  the  wires  should  not  be  less  than 


CHAP.  XXIV.]  Telegraphic  Lines.  343 

12  inches  vertically,  and  16  inches  horizontally,  with  20 
poles  per  mile. 

§  3.  No  line  can  be  perfectly  insulated.  On  land  lines 
no  leakage  occurs  from  the  wire  to  the  air,  but  at  every  pole 
there  must  with  the  best  construction  be  some  leakage, 
or,  in  other  words,  at  every  pole  there  is  a  connection  with 
the  earth..  The  resistance  of  this  connection  is  very  great 
when  the  wire  is  well  insulated,  and  small  when  there  is 
bad  insulation. 

The  wire  is  always  separated  from  the  wooden  pole  by  an 
insulator,  and  the  insulation  of  the  wire  depends  on  the  de- 
sign, material,  and  condition  of  these  insulators.  Glass  of 
certain  kinds  offers  the  greatest  resistance  to  conduction 
through  its  substance  of  any  known  material,  but  it  does  not 
answer  well  for  telegraphic  insulation,  because  surface  con- 
duction plays  by  far  the  greatest  part  in  the  leakage  from  a 
line,  and  glass  is  highly  hygroscopic,  i.e.  it  will  be  found 
covered  with  a  moist  film  in  most  states  of  the  weather. 
Ebonite  (hard  vulcanized  india-rubber)  has  a  high  insulation 
resistance  and  does  not  readily  become  damp,  but  rain  wets 
it  easily,  and  therefore  when  employed  for  insulators  it  is 
generally  covered  with  a  cap  of  some  other  material :  it  soon 
becomes  dirty  and  spongy  on  the  surface. 

Porcelain  of  certain  qualities  insulates  well ;  it  is  not 
nearly  so  hygroscopic  as  glass,  and  rain  runs  readily  from  its 
highly  glazed  surface.  The  glaze  insulates  still  better  than 
the  substance  of  the  porcelain,  but  in  some  specimens  is 
liable  to  crack  with  old  age,  when  its  value  is  lost. 

Brown  stoneware  is  an  excellent  and  cheap  material  for 
insulators  :  its  glaze  does  not  crack,  but  its  substance  has  not 
so  great  a  specific  resistance  as  highly  vitrified  porcelain. 
The  point  of  chief  importance  in  all  insulators  being  the 
condition  of  the  surface,  porcelain  and  stoneware  are  the 
favourite  materials ;  they  keep  clean,  do  not  change  with 
age  if  well  selected,  and  do  not  harbour  insects. 

The   form   most   used  approaches   thai  of  a  bell,  or  of 


344 


Electricity  and  Magnetism.    [CHAP.  XXIV. 


several  bells  one  inside  another.  In  Fig.  167  No.  i  shows 
Latimer  Clark's  double-bell  insulator;  No.  2  Varley's  insu- 
lator, made  in  two  pieces  ;  No.  3  the  French  cup  insulator, 
a  very  rudimentary  design ;  and  No.  4  Siemens'  insulator,  pro- 
tected and  supported  by  an  iron  cap. 

FIG.    167. 


The  objects  aimed  at  in  each  design  are  the  following : — 

i.  To  make  any  conducting  film  which  may  be  deposited 

on  the  surface  of  the  insulator  between  the  wire  and  the 

pole  as  long  as  possible,  because,  other  things  being  equal, 


CHAP.  XXIV.]  Telegraphic  Lines.  345 

its  resistance  increases  directly  as  its  length.  This  object 
is  attained  by  the  series  of  bells,  for  the  electricity  has  to 
run  down  outside  and  up  inside  each,  in  succession,  before 
getting  from  the  wire  to  the  pole. 

2.  To  make  the  cross  section  of  the  conducting  film  as 
small  as  possible.     With  this  object  the  insulator  is  kept  as 
small  in  diameter  as  is  consistent  with  other  conditions  of 
excellence. 

The  thickness  of  the  deposited  conducting  film  depends 
on  external  conditions,  but  the  larger  the  diameter  of  our 
bells  the  larger  will  be  the  cross  section  of  the  film,  i.e.  the 
ring  of  moisture  which  we  should  find  outside  and  inside 
each  ring  of  insulating  material  if  it  were  sawn  across  hori- 
zontally. 

3.  To  expose  one  portion  of  the  insulator  to  the  rain,  so 
that   it  may  be  cleansed  by  rain  from  dust,  salt,  smoke, 
spiders'  webs,  &c. 

4.  To  protect  another  portion  of  the  insulator  from  rain,  so 
that  when  the  outside  is  wet  the  inside  may  still  insulate. 
These  two  conditions  are  fulfilled  by  the  forms  i  and  2. 

5.  To  prevent  the  failure  of  part  of  the  insulator  from 
destroying   the   insulation.     With   this   object   some   good 
insulators  are  made  in  three  parts,  as  shown  in  Fig.  2 — two 
distinct  cups  and  a  vulcanite  covering  to  the  iron  supporting 
pin. 

6.  To  prevent  insects  from   settling  in  recesses.     This 
object  is  difficult  of  attainment,  and  limits  the  depths  of 
the  recesses  under  the  bells. 

7.  To  provide  strength  and  protection  against  malicious 
injury.    This  leads  to  the  adoption  of  metal  caps  as  in  Fig.  4. 

§  4.  Besides  leakage  from  the  wires  to  the  earth,  wires 
on  poles  are  subject  to  the  defect  of  more  or  less 
electrical  connexion  one  with  another,  by  the  surface  con- 
duction from  one  insulator  to  another.  To  prevent  this 
very  serious  inconvenience  a  wire  from  the  earth  is  led  up 
the  pole  and  across  every  portion  of  it  by  which  electricity 


346 


Electricity  and  Magnetism.    [CHAP.  XXIV. 


could  be  conducted  from  one  insulator  to  the  other.  A 
short  circuit  or  line  of  no  sensible  resistance  is  thus  pro- 
vided, so  that  all  leakage  finds  its  way  at  once  to  the  earth  ; 
simple  loss  weakening  the  transmitted  currents  causes  much 


FIG. 

168. 

||||||i|A                    B                  C 

DFX 

f'l'n'l                 j 

J                                            i 

I 

1                       ; 

less  inconvenience  than  cross  connections  by  which  the 
message  on  one  wire  finds  its  way  partly  into  its  neighbour. 
The  earth  wire  is  carried  above  the  pole  and  forms  a 
lightning  conductor. 

§  5.  The  insulation  resistance  of  a  line  is  measured  by 
FIG.  169.         measuring  the  resistance  experienced  at 
the  end  A  when  the  end  x  is  .  insulated, 
Fig.  168. 

The  resistance  thus  measured  is  not  the 
sum  of  the  several  insulation  resistances 
BE,,  c  E2,  D  E3,  &c.,  but  is  the  resistance 
due  to  the  circuits  A  B  Et,  B  c  E2,  CD  E3, 
&c.  arranged  in  multiple  arc  as  in  Fig. 
169.  We  can  calculate  this  total  resist- 
ance if  we  know  the  resistance  of  each 
elementary  part.  First  find  the  resistance  between  the  points 
D  and  E  due  to  a  double  arc  ;  next  add  this  resistance  to  that 
between  D  and  c ;  next  compound  the  resistance  so  found 
with  that  due  to  the  arc  c  E  ;  this  will  give  the  resistance 
due  to  all  the  conductors  between  c  and  E  ;  add  c  B  and 
proceed  as  before  till  the  resistance  due  to  all  conductors 
between  A  and  E  is  obtained. 

When  the  resistance  m  of  each  part  of  the  line  between 
two  poles  is  constant,  and  the  insulation  resistance  *  at 
each  pole  is  also  constant,  we  can  calculate  the  difference 


CHAP.  XXIV.]  Telegraphic  Lines.  347 

between  the  current  Q0  sent  into  the  line  and  that  received 
at  the  further  end  Qn  by  the  following  formula. 

/« 

Let  n  be  the  number  of  poles,  and  let  z  =  ^  <  where 

*=  2-718, 


Mr.  Varley  considers  no  line  well  insulated  for  which  the 
fraction  ™  is  greater  than  -g-^rJu-ff.  This  fraction  may  also  be 


defined  as  the  ratio  of  the  resistance  of  the  conductor  per  mile 
to  the  insulation  resistance  of  each  mile.     Qn  will  be  46  per 

cent,  of  Q0  in  a  line  of  400  miles  with  the  above  value  of  — 

§  6.  On  submarine  and  underground  circuits,  the  insula- 
tiqn  depends  wholly  on  the  resistance  to  conduction  across 
the  sheath  of  the  gutta  percha  or  india  rubber  covering. 
Surface  conduction  can  only  occur  at  the  two  extremities  of 
the  line,  and  unless  by  gross  neglect,  or  on  very  short  lines, 
cannot  be  a  sensible  cause  of  leakage. 

.Equation  i°  is  applicable  to  submarine  lines,  calling  m  the 
resistance  of  the  conductor  per  mile,  *  the  insulation  resist- 
ance of  each  mile,  and  n  the  length  of  the  line  in  miles. 

The  conductor  is  invariably  a  copper  strand,  and  the 
resistance  can  be  calculated  for  pure  copper  from  the  Table, 
§  14,  Chap.  XVI.  In  practice  from  five  to  eight  per  cent,  extra 
resistance  must  be  allowed  for  on  account  of  impurities. 

The  smallest  conductor  in  practical  use  for  sea  lines 
weighs  73  Ibs.  per  nautical  mile  of  2,029  yards  ;  the  largest 
yet  employed  (French  Atlantic)  weighs  400  Ibs. 

The  large  cores  require  nearly  an  equal  weight  of  gutta 
percha  as  a  covering,  and  the  lighter  conductors  require  a 
still  larger  proportion  of  insulator;  the  73  Ibs.  of  copper 
is  generally  covered  with  120  Ibs.  of  gutta  percha.  Hooper's 
india  rubber  is  sometimes  used  in  smaller  quantities  than 
gutta  percha. 

The  electrical  tests  applied  to  ascertain  the  quality  and 


348 


Electricity  and  Magnetism.     [CHAP.  XXTV. 


condition  of  the  materials  employed  in  the  case  of  submarine 
cables  are  —  the  measurement  of  the  resistance  of  the  core  ; 
the  measurement  of  the  resistance  of  the  insulator  to  con- 
duction from  the  copper  inside  to  water  outside  ;  and  the 
measurement  of  the  capacity  of  the  insulated  conductor  in 
microfarads.  The  methods  of  making  these  tests  have  been 
already  described. 

The  insulation  resistance  R  of  a  length  L  of  the  insulating 
core  measured  in  centimetres  is  given  in  terms  of  the  resist- 
ance R,  of  one  centimetre  cube  to  conduction  between  its 
opposed  faces  by  the  following  formula  : 


R  =  R8- 


27T     L 


'3 665  R,  log -^ 

L 


where    -  is  the  ratio  of  the  external  diameter  of  the  insula- 
d 

tor  to  that  of  the  enclosed  conductor.    From  this  equation  we 
have  the  resistance  Rk  of  one  knot  of  insulating  envelope  : 


I'( 


10° 

RS  is  what  was  called  in  Chap.  XV.  the  specific  resistance  of 
the  material. 

The  following  table  gives  the  value  of  R*.  and  RS  for 
some  important  cables  at  24°  C.  after  i  minute's  electrifi- 
cation. 


D 

T 

R* 

megohms. 

R, 

megohms. 

Malta  Alexandria  (first)     . 

2-95 

115 

4    x     io6 

Persian  Gulf,  mean  .... 

3-48 

IO    X      IO6 

Second  Atlantic,  mean 

3-28 

349 

342    x    io6 

French  Atlantic,  mean 

2-92 

234 

256    x    io6 

Hooper's  Persian  Gulf  (India  rubber),  > 
mean                                              \ 

8300 

7572    x    io6 

The  specific  gravity  of  gutta  percha  is  between  0-9693 
and  0-981.  The  weight  Wt  of  gutta  percha  per  knot  in  any 
case  is 


CHAP.  XXIV.]  Telegraphic  Lines.  349 


Where  D  and  d  are  measured  in  thousandths  of  an  inch. 
The  specific  gravity  of  Hooper's  rubber  is  about  1-176, 
and  the  constant  divisor  for  the  weight  of  Hooper's  material 
in  the  above  formula  is  400  instead  .of  480.  The  weight 
per  knot  wk  of  a  copper  strand  of  7  wires  such  as  is  used 
for  submarine  lines  is  in  Ibs. 


70*4 

§  7.  The  capacity  in  electrostatic  measurement  s  of  any 
length  of  wire  for  a  submarine  cable  maybe  calculated  by 
equation  6,  Chap.  V.  The  electromagnetic  capacity  s  is 
more  commonly  required,  and  we  know  (Chap.  VIII.  §  2) 


that  s  = -„  where  v  —   28-8    x    io9.     Hence  in  absolute 


electromagnetic  measure 


D    =      „         KL    ...       D 


4*6052  x  28-82  x  io18  xlog  ~d       3820  x  io18log^  ; 

and  calling  SM  the  capacity  in  microfarads,  we  have 
KL 

i>M   =     —=.  -  -T-.  -  JD  -o 

382  x  io4  log-^     ....     5 

This  value  of  SM  is  given  in  terms  of  L  measured  in  centi- 
metres :  practically  it  is  convenient  to  measure  the  length  in 
knots;  and  as  one  knot  is  equal  to  185,526  centimetres, 
(6087  feet),  we  have,  calling  Lk  the  length  in  knots, 

Cap.  of  cable  = 


Taking  the  value  of  K  for  gutta  percha  as  4*2  (vide  Chap.  V. 
§  5),  we  find  the  capacity  of  the  French  Atlantic  cable  to  be 
about  0-43  of  a  microfarad.  This  value  agrees  with  the 
result  of  direct  experiment  by  the  ballistic  method  (vide  §  5, 
Chap.  XVII.). 


350 


Electricity  and  Magnetism.     [CHAP.  XXIV. 


§  8.  Fig.  170  shows  a  cross  section  and  a  projection  of  the 
component  parts  of  the  Anglo-American  Atlantic  cable 
drawn  full  size.  In  the  centre  is  the  copper  strand  of  7 
wires  :  round  this  we  have  the  gutta  percha  envelope  covered 
by  a  serving  of  jute,  outside  which  there  are  ten  wires  of 

FIG.  170. 


FIG.  171. 


what  is  called  homogeneous  iron,  each  enveloped  in  fine 
strands  of  Manilla  hemp. 

Fig.  171  shows  the  more  common  type  of  cable,  in  which 
the  hemp-covered  steel  wires  are  replaced  by  iron  wires  of 
considerable  size.  These  iron  wires,  laid  on  as  shown  in  Fig. 


CHAP.  XXV.]     Faults  in  Telegraphic  Lines.  351 

171,  are  often  covered  with  one  or  two  outer  servings  of  jute 
and  a  compound  of  mineral  pitch,  silica,  and  tar,  known  as 
Clark's  compound. 


CHAPTER   XXV. 

FAULTS    IN    TELEGRAPHIC   LINES. 

§  1.  ANY  impediment  to  signalling  due  to  the  condition  of 
the  line  is  a  fault  Faults  are  of  three  kinds  : — i.  A  defect 
producing  bad  insulation.  2.  A  defect  producing  want 
of  continuity  in  the  line,  or  excessive  resistance.  3.  Contact 
between  two  neighbouring  conductors  used  for  separate 
messages. 

Defective  insulation  in  land  lines  may  be  due  to  cracked, 
dirty,  or  otherwise  defective  insulators,  or  to  contact  between 
the  line  and  some  conductor  in  connexion  with  the  earth. 
In  the  first  case  the  defect  may  be  distributed  over  a  great 
length  of  line.  We  can  determine  its  importance  by  elec- 
trical measurements.  In  the  second  case  the  fault  has  a 
definite  position,  and  we  can  determine  its  importance  and 
its  position  by  electrical  tests.  In  submarine  cables,  defective 
insulation  is  always  due  to  connexion  between  the  sea  and 
the  internal  conductor  at  one  or  more  definite  points.  The 
second  class  of  fault  implies  a  rupture  in  the  conducting 
wire  of  the  line  or  in  the  connexions  at  the  stations,  or  in  the 
connexions  with  the  earth  at  the  stations.  In  many  cases 
its  position  can  be  ascertained.  Frequently  the  first  and 
second  faults  co-exist :  i.e.  the  line  is  broken  and  its  end 
is  in  contact  with  the  earth.  The  third  class  of  fault  seldom 
arises  except  on  land  lines.  When  the  connexion  arises 
from  the  actual  contact  of  one  wire  with  another,  its  position 
is  easily  found. 

Tests  for  the  position  of  faults  can  generally  be  made 
more  accurately  on  submarine  lines  than  on  land  lines, 


352  Electricity  and  Magnetism.      [CHAP.  XXV. 

because  the  insulation  of  the  undamaged  portions  of  .the 
line  is  generally  better.  The  following  descriptions  refer 
especially  to  submarine  faults,  but  the  same  principles  are 
applicable  to  land  lines. 

§  2.  Let  there  be  a  fault  in  an  otherwise  well-insulated 
conductor,  involving  loss  of  insulation  at  one  point,  at  the 
distance  A  B,  Fig.  172,  from  station  A. 

If  the  connexion  at  B  with  the  earth  has  no  sensible  re- 
sistance, we  have  only  to  measure  the  resistance  A  B,  and 
divide  by  the  resistance  of  the  line  per  mile,  to  obtain  the 
distance  A  B  in  miles.  This  measurement  may  be  made  by 
the  Wheatstone  balance,  connected  as  shown.  A  D  and 
D  F  are  the  two  arms  of  the  balance,  F  E  is  the  box  of  resist- 

FIG.  172. 


ance  coils.  If  A  D  is  TV  of  D  F,  and  the  plugs  in  the  box 
between  F  and  E  arranged  so  as  to  give  1,500  units  when 
the  galvanometer  G  remains  undeflected  on  the  completion 
of  the  circuit,  then  ABE!  has  a  resistance  of  150  units; 
and  if  the  line  has  a  resistance  of  5  units  per  mile,  B 
is  30  miles  from  A.  It  is  always  desirable  to  insulate  the 
end  of  the  line  at  c  during  this  test.  We  can  easily  as- 
certain whether  the  resistance  of  B  Et  is  sensible  or  not,  by 
repeating  the  test  from  c.  If  by  the  second  test  we  find  a 
distance  B  c,  which,  added  to  A  B,  makes  up  the  whole  length 
of  the  line,  B  Et  can  have  no  resistance.  If,  on  the  other 


CHAP,  xxv.]     Faults  in  Telegraphic  Lines.  353 

hand,  the  sum  of  the  measurements  from  c  and  from  A  gives 
a  greater  length  than  A  c,  this  can  only  be  due  to  the  resist- 
ance of  the  fault  \  for  we  have  not  really  measured  the  re- 
sistance of  A  B  and  B  c,  but  of  A  B  -f-  BE!  and  B  c  +  B  Et. 
If  then  the  sum  of  the  two  measurements  exceeds  the  resist- 
ance A  c,  the  excess  will  be  equal  to  twice  the  resistance  of 
the  fault.  Let  m  be  the  resistance  measured  at  A,  n  the 
resistance  measured  at  c,  and  L  the  resistance  of  the  whole 
line. 


Then  A    B  = 


This  method  would  be  perfect  if  the  resistance  of  the  fault 
were  really  constant  while  the  resistances  m  and  n  were 
being  measured  ;  but  faults  usually  vary  very  much,  owing 
to  polarization  ;  and  hence,  except  with  great  faults  of  small 
resistance,  this  method  is  defective. 

§  3.  A  second  method  of  determining  the  resistance  A  B 
is  given  by  the  following  test,  on  the  assumption  that  the 
resistance  of  the  fault  is  constant  :  —  Measure  at  A  the  resist- 
ance m  of  the  line  when  c  is  insulated,  and  measure  the 
resistance  e  when  the  end  c  is  put  to  earth. 

Then  AB  +/=;#;  AB  +  —  -  —   =  e  and  A  B  +  B  c  =  L 

7  +  ifc 


therefore  A  B  =  e  —  V  (L  —  e)  (m  —  e)     .     .     .     2° 

This  test  is  even  less  trustworthy  than  the  preceding  one. 
By  taking  a  large  number  of  values  of  m  n  and  e  with 
different  poles  of  the  battery,  and  different  strengths  of 
battery,  and  choosing  the  smallest  values  obtained  as  those 
corresponding  with  one  and  the  same  minimum  value  of/, 
some  approach  to  accuracy  can  be  made.  Great  experience 
is  required  in  testing  to  enable  the  observer  to  judge  of  the 
nature  of  a  fault.  By  noting  the  polarization  obtained  with 
positive  and  negative  currents  of  different  strengths  the 
character  of  a  fault  can  generally  be  determined,  and  a 
guess  made  at  its  probable  resistance. 

A  A 


354  Electricity  and  Magnetism.       [CHAP.  XXV 

§  4.  When  there  is  a  well-insulated  return  wire  from  the 
distant  station  c  back  to  A,  the  position  of  a  leak  can  be 
determined  with  great  accuracy  by  what  are  called  loop  tests. 
The  observer  has  then  both  ends  of  a  complete  metallic 
circuit  before  him,  and  the  ratio  between  the  two  parts  which 
intervene  between  the  two  ends  and  the  fault  can  be  deter- 
mined by  several  methods,  all  independent  of  the  varying 
resistance  of  the  fault. 

Mr.  Varley  uses  a  differential  galvanometer  to  ascertain 
when  an  equal  current  runs  into  both  ends  of  the  metallic 
circuit  and  out  at  the  fault.  This  will  only  be  the  case 
when  the  resistance  between  the  galvanometer  and  the  fault 
is  the  same  by  both  roads.  This  condition  is  fulfilled  by 
adding  a  resistance  r  between  one  coil  of  the  galvanometer 

FIG.  173. 


and  the  defective  wire.  The  resistance  r  required  to  bring 
the  galvanometer  to  zero  is  obviously  equal  to  twice  the  re- 
sistance of  the  wire  between  the  distant  station  and  the 
fault. 

Perhaps  a  still  better  method  is  given  by  arranging  the 
VVheatstone  balance  as  shown  in  Fig.  173,  where  the  fault, 
supposed  to  be  at  o,  forms  part  of  the  circuit  connecting  the 
pole  c  to  the  metallic  conductor  subdivided  at  o. 

The  variation  of  the  resistance  of  the  fault  does  rot 
aifect  the  result :  it  will  indeed  cause  a  greater  or  less 
deflection  in  the  galvanometer  until  the  desired  balance  is 
effected,  but  it  will  not  alter  the  relative  resistances  of  the 


CHAP,  xxv  ]       Faults  in  Telegraphic  Lines. 


355 


several  parts  of  the  circuit  required  to  reduce  the  deflection 
to  zero.  The  test  is  made  by  adjusting  the  resistances  A 
and  B  until  no  deflection  is  obtained  ;  then,  calling  c  and  D 
the  resistances  of  the  conductors  separating  m  and  u  respec- 

tively from  the  fault,  we  have  —  =  -.     Then  the  resistance 

B       D 

of  c  +  D  being  called  L,  the  above  equation  gives  the  value  ot 


c  = 


AL 


§  5.  The  following  is  a  plan  for  determining  the  positioh 
of  a  fault  of  high  resistance  in  a  submarine  cable  by  a  simul- 
taneous test  at  each  end.  It  takes  into  account  the  uni- 
form leakage  from  each  knot  of  the  insulated  cable,  and 
can  be  carried  out  with  much  greater  synchronism  than  is 
possible  for  the  plans  described  in  §§  2  and  3,  above.  The 
connexions  are  shown  in  Fig.  174.  G  is  a  galvanometer  ; 

FIG.   \T». 


S  an  electrometer  at  the  same  station ;  B!  an  electro- 
meter at  the  distant  station,  where  the  end  of  the  sub- 
merged cable  is  insulated ;  the  battery  c  z  has  one  pole 
connected  with  the  galvanometer  G,  and  the  other  pole 
to  earth ;  let  k  be  the  resistance  of  the  unit  length  of  the 
conductor,  and  i  the  resistance  of  the  unit  length  of  insulated 
wire  to  conduction  across  the  sheath ;  then  let  /  be  the  length 
of  the  cable.  Let  A  be  the  distance  of  the  fault  from  the 
galvanometer  station ;  let  PJ  be  the  potential  at  the  distant 
station  ;  let  ?  be  the  potential  at  the  near  station,  and  C  the 
current  observed  on  the  galvanometer. 


356  Electricity  and  Magnetism.       [CHAP.  XXV. 

V    * 

„    D  =  P!  t-rt/  +  -  c.—  P 

Then  X  =  —  loge    -     ...          3". 
2  a  D 

The  measurements  must  be  made  in  one  consistent  system 
of  units.  Absolute  measurement  in  centimetres,  grammes, 
and  seconds  may  be  used  for  the  whole  series. 

The  test  requires  two  instruments  by  which  P  and  PJ  can 
be  measured  in  absolute  measure. 

§  6.  A  fault  of  insulation  in  a  submarine  cable  is  generally 
due  to  a  hole  in  the  dielectric.  This  hole  is  gradually  en- 
larged by  the  action  of  the  current,  although  the  polarization 
at  the  fault  often  seems  to  seal  it  up  for  a  time.  Rapid 
reversals  with  100  cells  or  more  tend  to  break  a  fault  down, 
i.e.  to  enlarge  it,  so  that  its  resistance  becomes  insignifi- 
cant. A  current  flowing  from  the  copper  to  the  sea 
apparently  seals  up  a  fault  better  than  the  opposite  current. 
It  causes  the  deposit  of  chloride  of  copper  and  oxygen, 
whereas  the  zinc  current  causes  a  deposit  of  salt  and  hydrogen. 
The  bubbles  of  gas  formed  under  great  pressure  in  time 
burst  the  film  of  deposited  salts,  and  the  fault  temporarily 
breaks  down.  When  this  occurs  with  the  negative  current, 
no  further  damage  occurs  in  general  than  a  slight  enlarge- 
ment of  the  fault ;  but  by  the  positive  current  a  slow  but 
certain  erosion  of  the  copper  is  produced,  which  always  ends 
in  producing  a  complete  and  sudden  loss  of  continuity  in 
the  conductor.  No  warning  is  given  of  the  impending  fatal 
injury  ;  for  so  long  as  the  slenderest  thread  of  copper  remains 
no  sensible  diminution  occurs  in  the  resistance  of  the  line. 
Signallers  prefer  to  keep  a  cable  positive  to  the  sea,  because 
they  get  better  signals,  the  currents  received  being  stronger, 


CHAP.  XXV.]         Faults  in  Telegraphic  Lines.  357 

and  less  liable  to  the  derangements  produced  by  the  sudden 
variations  of  a  fault.  The  practice  is,  however,  reprehensible. 
A  faulty  cable  should  always  be  kept  negative  relatively  to 
the  sea.  It  is  possible  to  send  very  good  signals  through  a 
cable  or  line  in  which  there  is  a  fault  of  such  magnitude 
that  its  resistance  is  far  less  than  that  of  the  conductor 
between  the  stations.  Nothing  is  absolutely  fatal  to  com- 
munication except  a  want  of  continuity  in  the  conductor. 

Sometimes  the  fault  is  made  by  the  presence  of  some 
foreign  body  in  the  insulator.  When  metal,  such  as  a  piece 
of  broken  wire,  is  driven  through  the  dielectric  connecting 
the  conducting  wire  with  the  sea,  or  with  the  metal  sheathing, 
a  fault  of  no  sensible  resistance  is  produced,  and  this  class 
of  fault  is  easily  recognised  by  the  absence  of  polariza- 
tion. 

§  7.  A  fault  of  the  second  class,  i.e.  involving  want  of 
continuity,  may  be  combined  with  one  of  the  first  class  : 
thus  the  cable  or  land-line  may  not  only  be  broken,  but  may 
be  in  more  or  less  perfect  connexion  with  the  earth  at  the 
fracture.  In  this  case  simultaneous  tests  at  both  ends  are 
impracticable.  We  can  only  measure  the  resistance  of  each 
unbroken  portion  of  the  cable,  and  guess  from  the  polariza- 
tion what  is  likely  to  be  the  fraction  of  the  whole  resistance 
observed  due  to  the  fault.  We  can  in  any  such  case  safely  fix 
a  maximum  distance  beyond  which  the  fault  cannot  lie.  With 
the  minimum  of  polarization  the  bare  copper  end  of  a  cable 
usually  has  a  resistance  equal  to  several  miles  of  the  con- 
ducting wire. 

A  fault  of  the  second  class  not  unfrequently  occurs  with 
perfect  insulation.  The  conductor  is  broken,  but  insulated 
at  the  fracture.  In  a  submarine  cable  the  distance  of  the 
insulated  fracture  can  then  be  measured  very  exactly  by 
measuring  the  capacity  of  the  cable  between  the  fracture  and 
the  shore.  The  capacity  per  mile  being  known,  this  test 
gives  the  distance  with  great  exactitude.  On  a  land  line  the 


35  8  Electricity  and  Magnetism.      [CHAP.  XXV. 

insulation  is  seldom  good  enough  to  allow  this  test  to  be 
rigorously  applied. 

§  8.  The  position  of  a  fault  of  the  third  kind — contact 
between  neighbouring  conductors — can  easily  be  fixed  if  the 
contact  is  local,  and  of  small  resistance.  We  need  only 
measure  the  resistance  of  the  loop  formed  by  the  contact, 
and  half  this  is  evidently  the  resistance  corresponding  to 
the  distance  of  the  fault.  When  the  contact  is  imperfect,  its 
position  can  be  very  accurately  determined  by  the  aid  of  a 
third  wire,  if  this  be  well  insulated  :  to  do  this,  treat  one  of 
ihe  two  wires  in  contact  as  an  earth,  leaving  it  uninsulated : 
and  by  the  loop  test  described  §  4  above,  fix  the  position  of 
the  point  of  contact  on  the  other  wire,  this  contact  being 
now  in  effect  an  ordinary  fault  of  the  first  class. 

The  position  of  the  contact  can  also  be  ascertained  with- 
out a  third  wire,  by  a  Wheatstone's  balance  test.  To  do 
this,  the  connections  are  arranged  as  follows,  Fig.  124:  r{ 
and  rm  are  resistance  coils,  r{l  and  riv  are  the  two  sub- 
divisions of  one  of  the  two  faulty  line  wires,  subdivided  at  E 
by  the  contact ;  the  point  B,  is  the  further  end  of  the  line, 
and  is  put  to  earth  ;  the  branch  r  is  made  up  of  the  galvano- 
meter, and  of  the  earth  at  B,;  the  wire  joining  the  battery 
with  E  is  the  second  line  wire  in  contact  with  the  first  at  E  ; 
the  further  end  of  the  second  line  is  insulated. 

Then,  calling  x  and  y  the  two  subdivisions  of  the  first  line 
wire,  we  have  x  =  ril9  y  =  r[v  and  r{  :  rm  =  x  :  y ;  whence, 
knowing  r\  and  rm,  x  and  y  can  be  found. 


CHAP.  X XV I.  ]     Applications  of  Electricity.  359 


CHAPTER  xxvi. 

USEFUL   APPLICATIONS    OF    ELECTRICITY,  OTHER   THAN 
TELEGRAPHIC. 

§  1.  ELECTRICITY  has  been  applied  in  so  many  ways  to  the 
useful  arts  that  a  large  separate  treatise  might  be  written  on 
these  applications.  In  this  book  a  few  only  of  these  appli- 
cations can  be  mentioned,  and  these  must  be  very  cursorily 
described,  under  the  heads  of  Electro-Metallurgy,  Electric 
Light,  Medical  Applications,  the  Firing  of  Mines,  Clocks, 
governors  and  chronoscopes. 

ELECTRO-METALLURGY. 

§  2.  In  metallurgy  electricity  finds  a  threefold  applica- 
tion, i.  To  electro-plating,  such  as  gilding  or  silvering 
objects.  2.  To  the  reproduction  by  metallic  casts  of 
objects  of  any  form.  3.  To  the  reduction  of  metals 
from  their  ores.  When  our  object  is  to  coat  a  metal 
with  a  thin  metallic  film  of  some  other  metal,  we  immerse 
the  object  to  be  coated  in  a  solution  of  some  salt  of  the 
metal  to  be  deposited.  We  pass  a  current  from  the  bath 
to  the  object,  so  as  to  decompose  the  salt  and  deposit  the 
metallic  positive  ion  on  the  object,  which  is  a  negative  elec- 
trode. By  the  choice  of  a  proper  salt,  a  proper  strength  of 
solution,  and  a  proper  strength  of  current,  the  film  can  be  made 
adhesive.  When  copper  objects  are  to  be  gilt,  they  are 
treated  as  follows  : — They  are  first  heated,  to  dispel  any  fatty 
matter  from  their  surface ;  they  are  next  plunged  while 
still  hot  in  very  dilute  nitric  acid,  which  removes  any  coating 
of  oxide  or  suboxide  of  copper ;  they  are  then  rubbed  with 
a  hard  brush,  washed  in  distilled  water,  and  dried  in  gently 
heated  sawdust.  They  are  still  further  cleaned  by  being 
rapidly  immersed  in  ordinary  nitric  acid,  and  next  in  a 
mixture  of  nitric  acid,  bay  salt,  and  soot.  The  objects  thus 


360  Electricity  and  Magnetism.     [CHAP.  xxvi. 

prepared,  so  as  to  have  a  uniformly  clean  metallic  surface, 
are  immersed  in  a  bath  containing  a  solution  of  some  salt 
of  gold. 

The  objects  are  attached  to  the  zinc  pole  of  a  battery 
consisting  of  three  or  four  elements,  the  other  pole  of  which 
is  connected  with  an  electrode  of  gold  also  plunged  in  the 
bath.  The  passage  of  the  current  decomposes  the  salt, 
deposits  gold  on  the  object,  and  causes  the  dissolution  of 
an  equal  quantity  of  gold  from  the  gold  electrode.  The 
time  required  for  the  operation  depends  on  the  thickness  of 
coating  required.  One  grain  of  gold  and  10  grains  of 
cyanide  of  potassium  in  every  200  grains  of  water  form 
a  suitable  bath.  Silver,  bronze,  brass,  German  silver,  and 
some  other  metals  can  be  directly  gilt  in  this  manner  ;  but 
in  order  to  gild  iron,  steel,  zinc,  tin,  or  lead,  it  is  found 
necessary  to  electroplate  them  first  with  copper.  The  bath 
from  which  copper  is  deposited  is  a  saturated  solution  of 
sulphate  of  copper.  The  positive  electrode  must  then  be 
a  copper  plate.  A  bath  for  the  deposition  of  silver 
consists  of  two  grains  of  cyanide  of  silver  and  two  parts  of 
cyanide  of  potassium  in  every  two  hundred  grains  of  water ; 
the  positive  electrode  must  be  a  silver  plate. 

§  3.  The  reproduction  of  objects  in  metal  by  electricity  is 
effected  by  a  thick  deposit  of  the  metal  in  a  mould,  the  sur- 
face of  which  has  been  so  treated  as  to  be  a  good  conductor. 
The  deposit  is  obtained  from  a  bath  by  the  passage  of  a 
current,  precisely  as  the  deposit  required  for  electro-plating 
is  produced. 

The  mould,  if  made  of  metal,  should  be  slightly  coated  with 
some  fatty  substance.  A  brush  rapidly  passed  through  a  smoky 
flame,  and  then  used  as  it  were  to  dirty  the  mould,  is  said 
to  be  sufficient  to  prevent  adhesion.  Ganot  mentions  Street's 
fusible  alloy,  consisting  of  5  parts  of  lead,  8  of  bismuth,  and 
3  of  tin,  as  suitable  for  moulds  of  metallic  objects.  Stearine 
is  used  to  prepare  moulds  of  plaster  objects  ;  these  are 
first  immersed  in  melted  stearine  and  withdrawn  quickly  ; 


CHAP.  XXVL]     Applications  of  Electricity.  361 

some  of  the  stearine  is  absorbed  by  the  pores  of  the  plaster  ; 
the  surface  is  next  coated  with  graphite  or  with  black  lead 
rubbed  on  with  a  brush.  The  stearine  mould  can  then 
be  taken.  The  interior  surface  of  the  mould  is  covered 
with  graphite  to  make  it  conduct. 

Gutta  percha  moulds  may  be  prepared  by  pressing  gutta 
percha  heated  in  warm  water  against  the  surface  of  the  object 
to  be  copied,  which  should  previously  be  covered  with 
graphite  to  prevent  adhesion.  The  mould  must  also  be 
coated  with  graphite  to  make  it  conduct.  Any  of  these  moulds, 
used  as  a  negative  electrode  in  a  bath  of  sulphate  of 
copper,  will  become  filled  with  a  copper  deposit,  which  re- 
produces the  original  object.  This  process  is  of  great  use  to 
printers.  Copper  plates  are  beautifully  reproduced  by  its 
means. 

§  4.  The  reduction  of  ores  has  never  been  carried  out  on 
any  large  scale,  but  several  of  the  rarer  metals  have  only 
become  known  to  us  by  the  decomposition  of  their  salts 
under  the  action  of  the  electric  current.  Davy  obtained 
potassium  for  the  first  time  by  decomposing  a  slightly 
moistened  fragment  of  hydrate  of  potash  by  a  current  from 
200  or  250  cells.  Sodium  can  be  obtained  in  a  similar  way  ; 
but  other  methods  are  now  known,  which  are  commercially 
preferable. 

Barium,  calcium,  magnesium,  aluminium,  &c.,  can  be  ob- 
tained by  electrolytic  methods. 

The  ores  of  silver,  lead,  and  copper  have  been  treated  by 
electric  processes,  many  details  of  which  will  be  found  in  the 
4  Traite  d'Electricite  et  de  Magne'tisme,'  by  Messrs. Becquerel, 
vol.  ii. 

ELECTRIC   LIGHT. 

§  5.  When  the  points  of  two  pencils  of  charcoal  or  graphite, 
attached  by  thick  wires  to  the  two  poles  of  a  galvanic  batter)7 
of  forty  or  fifty  Grove's  elements,  are  placed  for  a  moment  in 


362  Electricity  and  Magnetism.     [CHAP.  XXVI. 

contact  and  then  withdrawn,  so  as  to  remain  about  one 
eighth  of  an  inch  distant,  a  current  will  flow  round  the  circuit 
crossing  the  arc  from  pencil  to  pencil,  and  at  this  spot 
emitting  a  most  brilliant  light. 

The  name  Toltaic  arc  is  often  used  to  designate  that  por- 
tion of  a  continuous  current  where  there  is  a  gaseous  con- 
ductor. The  voltaic  arc  is  in  most  cases  luminous.  Its 
colour  depends  on  the  gas  traversed,  and  its  intensity  is 
closely  connected  with  the  density  of  the  gas.  With  rare- 
fied gases,  as  in  the  Geissler  tubes  described  above,  a  com- 
paratively feeble  glow  is  obtained  ;  in  air,  the  intensity  of 
the  electric  light  may  be  as  great  as  ^  that  of  sun-light, 
according  to  experiments  of  Fizeau  and  Foucault.  The 
air  is  much  heated  at  the  point  of  passage,  and  its  resist- 
ance thereby  reduced  ;  if  the  current  be  momentarily  inter- 
rupted, the  E.  M.  F.  of  the  battery  will  be  unable  to  re- 
establish the  voltaic  arc,  unless  the  points  are  again 
brought  very  close  or  into  contact,  to  be  withdrawn  as 
before  when  the  current  has  been  established  ;  the  reason 
being  that  the  E.  M.  F.  which  is  sufficient  to  send  the 
current  across  hot  air  is  insufficient  when  this  air  is 
cooled.  The  carbon  of  the  pencils  is  consumed  in  the 
production  of  the  light.  The  positive  electrode  is  much 
more  rapidly  consumed  than  the  negative  electrode,  and 
becomes  hollow  at  the  point.  In  order  to  render  the  light 
available  for  practical  use,  the  graphite  pencils  must  be  held 
in  a  lamp,  so  constructed  that  the  opening  between  the 
points  remains  sensibly  in  one  place.  In  these  lamps  there 
must  therefore  be  a  feed  supplying  the  pencils  in  the  ratio 
Jn  which  they  are  found  to  be  consumed.  The  lamp  must 
also  be  furnished  with  some  contrivance  by  which,  if  the 
voltaic  arc  is  extinguished  from  any  cause,  the  graphite 
rjoints  will  instantly  fall  together,  re-establish  the  arc,  and 
again  separate  to  the  normal  distance  for  the  greatest  inten- 
sity of  light.  Lamps  fulfilling  these  conditions  more  or  less 
perfectly  by  means  of  electro-magnetic  gearing  have  been 


CHAP.  XXVI.]      Applications  of  Electricity.  363 

invented  by  Mr.  F.  H.  Holmes,  M.  Serrin,  M.  Dubosc, 
and  others. 

Mr.  Holmes's  lamp  has  been  used  for  lighthouse  illumi- 
nation with  success. 

An  electromotive  force  of  about  eighty  volts  is  apparently 
the  least  with  which  a  good  electric  light  can  be  produced, 
and  the  resistance  of  the  circuit  (exclusive  of  the  voltaic 
arc)  must  not  much  exceed  12  or  15  ohms.  Sir  William 
Thomson  has  produced  a  good  light  with  eighty  Daniell's 
cells  of  the  construction  and  dimensions  described  §  12, 
Chap.  XV.  These  cells  remained  in  good  condition  for 
several  months,  so  that  the  light  could  be  obtained  at  any 
moment  by  merely  closing  a  circuit.  Grove's  cells  will 
only  act  well  for  a  few  hours  after  being  filled,  and  give  out 
noxious  fumes. 

Mr.  Waring  produces  an  intense  electric  light  by  the  in- 
candescence of  mercury  vapour.  The  current  is  passed 
along  a  thin  stream  of  mercury,  which  it  volatilizes.  The 
mercury  is  hermetically  enclosed.  This  light  has  a 
greenish  tinge.  A  rapid  succession  of  sparks  from  a 
Ruhmkoff  coil  will  also  produce  a  somewhat  feeble  light. 

The  electric  light  may  be  made  use  of  in  photography, 
and  the  examination  of  its  spectrum  presents  many  points 
of  great  interest  to  the  physicist. 

FIRING   OF    MINES. 

§  6.  This  is  effected  by  passing  a  current  through  a  film  of 
semi-insulating  substance,  which  becomes  red  hot,  and  fires 
a  detonating  mixture  or  gunpowder.  A  fuse  is  prepared  to 
which  two  insulated  wires  are  led.  The  ends  of  these 
wires  are  imbedded  in  a  thin  solid  gutta  percha  rod  :  they 
do  not  join,  but  end  in  a  little  layer  of  the  priming  com- 
position, which  is  an  intimate  mixture  of  subsulphide  of 
copper,  subphosphide  of  copper,  and  chlorate  of  potassium. 
The  whole  is  surrounded  by  gunpowder.  A  feeble  current 
will  not  heat  the  priming  composition  to  redness,  but  a 


364  Electricity  and  Magnetism.     [CHAP.  XXVI. 

powerful  current,  even  if  short,  will  develop  enough  heat  by 
its  passage  to  ignite  the  powder.  The  current  is  generally 
produced  by  the  discharge  of  a  condenser,  and  this  con- 
denser is  often  charged  by  a  frictional  electric  machine.  A 
vulcanite  plate  machine  as  designed  by  Ebner  is  much  used 
with  a  condenser  consisting  of  a  sheet  of  india  rubber  with 
tinfoil  armatures  rolled  up  so  as  to  form  a  cylinder.  A 
magneto-electric  current  or  a  battery  current  may  be  used. 
When  the  mine  or  torpedo  is  to  be  fired  by  the  discharge  of 
a  condenser,  a  fine  wire  is  better  than  a  thick  one,  in  order 
that  the  capacity  of  the  conductor  may  be  small :  with  the 
same  object  the  thickness  of  the  dielectric  should  be  con- 
siderable, and  the  very  best  insulation  is  necessary. 

The  detonating  mixture  may  also  be  fired  by  heating 
to  redness  a  fine  platinum  wire  stretched  between  the  two 
ends  of  the  copper  wires  :  the  platinum  wire  should  be  coated 
with  fulminate  of  mercury.  A  voltaic  battery  is  required  with 
this  arrangement,  which  has  the  double  advantage  that  the 
condition  of  the  conductors  can  from  time  to  time  be  tested 
by  feeble  currents  which  will  not  explode  the  charge,  and 
that  it  allows  several  insulated  conductors  to  be  laid  in  one 
cable,  which  plan  cannot  be  followed  when  the  mine  is 
fired  by  the  discharge  from  a  condenser,  owing  to  the  power- 
ful current  then  induced  in  the  neighbouring  wires,  which 
would  fire  all  the  mines  whenever  a  current  was  passed  along 
a  single  wire.  The  platinum  fuse  can  be  fired  when  the 
insulation  of  the  conductors  is  very  defective. 

MEDICAL   APPLICATIONS. 

§  7.  Electricity  in  its  passage  through  the  body  may  produce 
very  marked  physiological  effects.  The  simple  passage  of  a 
current  from  one  hundred  cells  produces  a  somewhat  dis- 
agreeable disturbance  or  tingling  at  the  point  where  it  enters  or 
leaves  the  body.  This  feeling  is  considerably  more  intense  at 
the  moment  when  the  current  begins  and  ceases  than  at  any 
other  time.  When  a  powerful  current  of  very  short  duration 


CHAP.  XXVI. ]     Applications  of  Electricity.  365 

is  sent  through  the  body,  as  from  a  Leyden  jar  of  moderate 
size  charged  to  the  potential  of  several  hundred  volts,  the 
disturbance  is  felt  throughout  the  frame,  and  is  well  known 
as  an  electric  shock.  The  disturbance  produced  may  be  so 
great  as  to  produce  illness  or  death,  and  many  persons  who 
are  killed  by  lightning  are  killed  by  the  simple  shock  re- 
sulting from  the  sudden  discharge  of  electricity  from  their 
bodies,  which  had  been  inductively  electrified  from  the 
clouds ;  the  lightning  passing  from  cloud  to  cloud  discharges 
these,  and  the  escape  of  the  electricity  from  the  body  pre- 
viously charged  produces  the  shock.  The  rapid  succession 
of  currents  produced  by  rotating  magneto-electric  arrange- 
ments produce  a  singular  numbness  if  passed  through  the 
body,  so  that  a  man  holding  two  electrodes  from  which  these 
short  rapidly  alternating  currents  flow  cannot  let  them  fall, 
but  holds  them  convulsively.  The  very  first  discovery  of  the 
electric  current  by  Galvani  was  due  to  the  contraction  of  a 
muscle  of  a  frog  under  the  influence  of  the  current.  From 
all  these  facts  it  cannot  be  doubted  that  electricity  may  be 
of  use  as  a  curative  agent ;  the  medical  man  may  find  in  it  a 
means  of  producing  important  modifications  in  the  condi- 
tion of  the  body ;  but  the  author  is  unable  to  speak  with 
any  confidence  of  the  applications  as  yet  made  of  this  agent. 
Rapidly  alternating  magneto  currents  are  the  most  popular, 
but  he  is  not  aware  that  thoroughly  scientific  experiments  have 
been  made  on  the  effects  produced,  or  on  the  real  magnitude 
of  the  currents  employed.  Valuable  results  may  have  been 
and  may  be  attained,  but  it  is  for  medical  men  to  decide 
how  far  these  have  or  have  not  been  the  results  of  some 
happy  accident.  The  application  of  electricity,  unhappily, 
can  easily  be  made  the  subject  of  quackery  without  de- 
tection. 

The  actual  cautery  can  be  applied  by  platinum  wire 
heated  by  an  electric  current  in  parts  of  the  body  which 
could  not  be  reached  in  any  other  way. 


366  Electricity  and  Magnetism.         [CHAP.  XXVL 


CLOCKS,    GOVERNORS   AND    CHRONOSCOPES. 

§  8.  There  are  many  other  useful  applications  of  electricity. 
Mr.  Alexander  Bain  drives  clocks  by  a  small  current  acting 
on  a  propelment,  the  speed  of  which  is  regulated  by  a 
pendulum.  The  propelment  acts  like  the  propelment  of  the 
dial  telegraph  instruments.  The  same  inventor  followed 
by  others  controls  distant  clocks  from  one  standard  clock 
by  electro-magnets  set  in  action  by  currents.  The  pendu- 
lum of  the  distant  clock  oscillates  freely  if  keeping  perfect 
time,  but  is  slightly  retarded  or  accelerated  by  an  electro- 
magnet if  before  or  behind  time.  Time  guns  or  other  time 
signals  are  also  given  from  observatories  by  the  aid  of 
electric  currents. 

Electricity  is  made  use  of  in  one  form  of  governor  to 
regulate  the  speed  of  machinery.  When  the  speed  is  ex- 
cessive, the  governor  balls  by  their  divergence  complete 
a  contact  which  permits  a  current  of  electricity  to  produce 
friction  by  the  action  of  an  electro-magnet. 

Electricity  is  made  use  of  to  light  the  gas  in  one  species  of 
motor  gas  engine,  and  electric  sparks  have  been  used  to 
light  gas  lamps. 

Electric  chronoscopes  measure  time  to  thousandths  of  a 
secondhand  by  their  aid  the  speed  of  projectiles  is  ascer- 
tained :  the  plan  in  general  being  that  the  projectile  at  one 
part  of  its  path  interrupts  one  circuit,  and  at  another  part  a 
second  circuit,  by  cutting  wires.  The  interruptions  deter- 
mine sparks  which  leave  their  record  on  prepared  paper  or 
a  metallic  surface,  moving  with  known  velocity  :  the  distance 
between  the  records  of  the  sparks  serves  therefore  to 
measure  the  time  occupied  by  the  projectile  in  passing  from 
one  wire  to  the  next.  In  this  little  treatise  these  and  many 
other  important  applications  can  barely  be  enumerated. 
As  the  science  becomes  more  familiarly  known,  the  extent 
and  number  of  useful  applications  will  day  by  day  increase. 


CHAP.  XX VIL]        Atmospheric  Electricity.  367 

CHAPTER  XXVII. 

ATMOSPHERIC   AND   TERRESTRIAL    ELECTRICITY. 

§  1.  NOT  much  is  known  of  the  distribution  of  electricity 
on  the  surface  of  the  earth.  According  to  Sir  William 
Thomson  the  most  probable  distribution  is  analogous  to  that 
which  would  be  produced  if  the  earth's  surface  generally  were 
charged  with  negative  electricity  held  as  a  charge  on  the  inner 
armature  of  a  condenser,  the  outer  armature  of  which  was 
in  the  upper  regions  of  the  atmosphere,  the  lower  part  of 
which  acts  as  the  dielectric.  Electrified  masses  of  air  moving 
at  no  great  distance  from  the  earth's  surface  are  continually 
altering  the  distribution  of  electricity,  which  is,  however,  gene- 
rally found  to  be  negative  on  the  earth's  surface.  The 
modes  of  investigating  the  density  of  electrification  and  the 
sign  of  the  electricity  at  the  earth's  surface  are  analogous  to 
the  method  of  the  proof  plane.  Some  conductor  in  contact 
with  the  earth  is  insulated,  brought  indoors,  and  the  sign 
of  its  electrification  ascertained  by  an  electrometer.  We 
here  speak  of  the  electrification  of  the  surface,  not  of  the 
potential,  at  points  of  the  air  which  must  be  separately 
investigated.  We  cannot  treat  air  as  we  can  the  earth, 
because  it  is  an  insulator,  and  will  not  part  with  its  elec- 
tricity to  any  conductor  analogous  to  a  proof  plane. 

§  2.  The  potential  of  the  earth's  surface  is  assumed  as  the 
zero  or  datum  from  which  all  other  potentials  are  measured ; 
nevertheless  we  know  that  the  potentials  of  different  places 
on  and  in  the  earth  differ  considerably,  sometimes  to  the 
extent  of  several  hundred  volts,  though  this  is  rare.  We 
obtain  this  information  from  the  currents  observed  to  flow 
through  wires  joining  parts  of  the  earth  widely  separated. 
These  currents  being  known,  and  the  resistance  of  the 
circuit  being  known,  the  E.  M.  F.  due  to  differences  of  poten- 
tial between  the  ends  of  the  wire  can  be  inferred  with 


368  Electricity  and  Magnetism.    [CHAP.  XXVII. 

certainty.  The  difference  of  potential  between  the  two 
sides  of  the  Atlantic  is  often  not  more  than  one  or  two 
volts,  and  generally  points  joined  by  the  sea  are  nearly  at 
one  potential.  This  condition  is,  however,  liable  to  be  dis- 
turbed from  time  to  time,  and  these  disturbances  are 
called  electric  storms.  Statistics  of  the  distribution  of  po- 
tential over  the  earth's  surface  have  not  yet  been  compiled. 

§  3.  Any  conductor  at  the  end  of  which  a  flame  is 
burning,  or  any  small  pipe  from  which  water  drops,  will  very 
soon  acquire  the  potential  of  the  air  where  the  flame  burns 
or  the  water  is  dropping ;  for  if  there  is  any  difference  of 
potential  between  the  conductor  and  the  air  near  the  flame 
or  tube  end,  it  will  cause  an  accumulation  of  electricity  at 
the  flame  or  tube  end,  and  this  electricity  will  then  ba 
conveyed  away  by  the  particles  flying  off  in  the  flame  or  by 
the  drops  of  water  until  there  is  no  difference  of  potential 
between  the  conductor  and  the  neighbouring  air. 

This  fact  enables  us  to  measure  the  potential  of  the  air  at 
any  point,  or,  in  other  words,  to  compare  its  potential  with 
that  of  the  earth.  To  do  this,  a  conductor  having  a  flame 
or  water-dropping  arrangement  at  one  end  is  connected  with 
one  pair  of  quadrants  of  the  reflecting  electrometer ;  this 
pair  of  quadrants  is  thereby  brought  to  the  potential  of  the 
air  at  the  spot  to  be  tested.  The  other  pair  is  connected 
with  the  earth,  and  the  difference  of  potentials  is  then 
measured  by  the  deflection  of  the  electrometer  in  the  usual 
way.  Other  forms  of  electrometer  may  be  used.  Sir  William 
Thomson  found  that  the  potential  of  the  air  varied  very 
rapidly  near  the  surface  of  the  earth.  Thus  he  has  observed 
a  difference  of  potential  between  the  earth  and  the  air  nine 
feet  above  it,  equal  to  430  volts  in  ordinary  fair  weather,  and 
in  breezes  from  the  east  and  north-east  as  great  a  difference 
as  this  per  foot  of  air.  The  potential  is  perpetually  fluc- 
tuating, even  in  fair  weather.  Instruments  have  been  in 
action  for  some  time  at  Kew  and  elsewhere,  recording  con- 
tinuously the  differences  of  potential  between  the  earth  and 


CHAP.  XXVIII.]     The  Mariner's  Compass.  369 

one  point  in  the  air.  The  potential  of  the  air  appears  to  be 
generally  positive  in  fine  weather,  and  negative  only 
during  broken  or  rainy  weather. 

§  4.  The  distribution  of  magnetic  force  on  the  surface  of 
the  earth  has  already  been  alluded  to  in  Chap.  VII.  '  It  is 
conceivable  that  this  force  may  be  wholly  due  to  currents 
flowing  round  the  earth,  and  maintained  by  the  thermo- 
electric action  due  to  the  sun,  or  to  some  other  cause  con- 
nected with  the  rotation  of  the  earth.  Observation  does 
not,  however,  as  yet  enable  a  decided  opinion  to  be  given 
on  this  point. 


CHAPTER  XXVIII. 

THE  MARINER'S  COMPASS. 

§  1.  The  mariner's  compass  'consists  of  a  card  pivotted  on 
a  vertical  axis,  and  directed  by  having  on  its  lower  surface 
one,  two,  four,  or  more  parallel  magnets  with  similar 
poles  pointing  in  similar  directions.  The  magnets  being 
free  to  turn  in  a  horizontal  plane,  place  themselves  in  the 
magnetic  meridian.  The  object  of  using  several  magnets 
is  to  increase  the  magnetic  moment  for  a  given  weight  of 
steel.  The  upper  surface  of  the  card  is  divided  into  degrees 
and  also  into  thirty- two  parts,  each  containing  11°  15';  the 
thirty-two  rays  indicate  the  thirty-two  points  of  the  com- 
pass ;  the  line  joining  the  north  and  south  points  is  parallel 
to  the  axes  of  the  magnets.  The  north  and  south  line 
indicates  the  magnetic  meridian  at  each  place.  As  was 
shown  in  Chapter  VII.,  the  declination  varies  at  different  times 
and  at  different  places.  The  declination  of  the  particular 
place  at  the  particular  time  must  be  known  by  means  of 
charts  or  otherwise  before  the  true  north  or  any  other  true 
course  can  be  determined  by  the  aid  of  the  compass. 

§  2.  The  presence  of  any  iron  or  steel  in  the  neighbour- 
hood of  the  compass  alters  the  direction  of  the  lines  of 
force  in  the  magnetic  field,  and  causes  what  is  termed  a 

B  B 


37°  Electricity  and  Magnetism.  [CHAP,  xxvill. 

deviation  of  the  north  and  south  line  from  the  magnetic 
meridian.  In  wooden  ships,  by  a  little  care  in  placing  the 
compass  properly,  deviation  errors  of  any  practical  moment 
may  be  wholly  avoided,  but  in  iron  ships  they  must  be 
partly  allowed  for  and  partly  compensated.  The  deviation 
in  an  iron  ship  is  due  to  two  causes — ist,  the  permanent 
magnetism  of  the  ship ;  2nd,  the  magnetism  induced  by  the 
earth's  magnetic  force.  We  can  compensate  for  the  effect  of 
the  permanent  magnetism  by  properly  placing  a  permanent 
steel  magnet  in  the  neighbourhood  of  the  compass,  exerting 
an  equal  and  opposite  couple  to  that  due  to  the  ship. 

We  cannot  compensate  or  can  only  very  imperfectly  com- 
pensate for  the  effect  of  induced  magnetism,  because  it  is 
impracticable  to  arrange  a  soft  iron  structure  near  the  com- 
pass, such  that  its  induced  magnetism  shall  have  an  opposite 
and  equal  effect  to  that  of  the  ship.  The  induced  magnetism 
varies  as  the  ship  turns  round  horizontally.  Thus  when  she 
bears  north  or  south,  her  magnetic  moment  is  much  greater 
than  when  east  or  west.  By  testing  experimentally  in  port 
the  deviation  on  each  course,  a  correction  is  obtained  for  that 
particular  neighbourhood.  The  ship's  induced  magnetism 
also  varies,  however,  as  the  direction  and  intensity  of  the 
earth's  magnetic  force  varies  ;  and  no  safe  allowance  can 
be  made  for  errors  resulting  from  this  cause.  Moreover 
the  induced  magnetism  varies  as  the  ship  rolls,  and 
(to  a  much  less  extent)  as  she  pitches.  The  heeling  error 
can  be  compensated,  as  was  shown  by  the  late  Mr. 
Archibald  Smith.  The  Admiralty  Compass  Manual,  written 
by  that  gentleman  in  concert  with  Captain  Evans,  R.N., 
should  be  consulted  by  all  who  wish  to  understand  the 
mariner's  compass.  The  mathematical  and  practical  in- 
vestigations of  Mr.  Smith  have  been  of  the  very  highest 
utility  in  adding  both  to  our  scientific  knowledge  and  to 
the  practical  utility  of  the  mariner's  compass. 

T\iz prismatic  compass  and  azimuth  compass  are  compasses 
fitted  with  contrivances  by  which  the  bearings  of  objects  can 
be  taken. 


APPENDIX 

ON   THE 

TELEPHONE  AND   MICROPHONE. 


IN  1837,  Page  discovered  that  the  magnetisation  and  de- 
magnetisation of  iron  was  accompanied  by  sound.  P.  Reiss 
of  Friedrichsdorf  in  1861  invented  an"  arrangement  by 
which  a  musical  note  at  one  end  of  a  telegraphic  wire  was 
reproduced  at  the  other  end.  This  he  effected  by  causing 
the  vibration  of  a  reed  to  make  and  break  a  circuit  at  the 
sending  end ;  the  current  was  therefore  transmitted  once  for 
every  period  of  the  reed's  vibration  ;  this  current  magnetised 
a  small  iron  core,  and  at  each  transmission  a  click  was  pro- 
duced, not  in  itself  musical,  but  producing  the  effect  of  a 
definite  note  on  the  ear  when  repeated  a  definite  number 
of  times  per  second.  When  the  reed  vibrated  so  as  to  give 
a  certain  note,  the  same  note  was  heard  at  the  other  end  of 
the  line.  The  quality  of  the  sound  received  had  no  resem- 
blance to  the  quality  of  the  sound  produced  by  the  sending 
reed.  One  period  of  the  reed's  vibration  corresponded  to 
one  periodic  change  in  the  receiving  magnet,  but  beyond 
this  there  was  no  correspondence  between  the  reed  and  the 
magnet.  It  is  not  quite  certain  to  this  day  what  causes  the 
click  heard  when  the  core  is  magnetised  or  demagnetised  ; 
this  sound  may  simply  be  due  to  the  shortening  or  length- 
ening of  the  core  as  a  whole,  but  it  is  also  possible  that  it 
may  be  due  to  more  complex  molecular  changes.  It  might 
be  supposed  that  the  hearer  should  hear  a  note  one  octave 

B  B  2 


3/2  Electricity  and  Magnetism. 

higher  than  that  sent,  but  this  is  not  the  case ;  the  ear 
treats  the  whole  periodic  change  in  the  magnet  due  to  one 
vibration  of  the  reed  as  a  single  periodic  sound. 

The  apparatus  employed  by  Reiss  may  be  called  a  tele- 
phone, since  by  its  means  one  feature  of  a  given  sound  was 
reproduced  at  a  distance  by  the  intervention  of  electricity. 
This  apparatus  did  not  and  cannot  reproduce  more  than  one 
feature,  namely  fat  pitch  of  the  note.  Not  only  is  it  impos- 
sible by  its  use  to  reproduce  articulate  sounds  or  the  quality 
of  a  musical  note,  but  even  a  change  in  the  loudness  of  the 
note  at  the  sending  end  produces  little  or  no  change  in  the 
loudness  of  the  note  heard  at  the  receiving  end. 

Mr.  C.  F.  Varley  in  1870  showed  that  a  sound  analogous 
to  that  produced  by  the  magnetisation  of  iron  could  be 
produced  by  the  charging  or  discharging  of  a  Ley  den  jar  or 
condenser.  The  noise  is  apparently  due  to  the  rearrange- 
ment of  the  particles  of  the  dielectric  under  a  changed 
condition  of  stress.  Mr.  Varley  showed  that  this  property 
of  the  condenser  might  be  made  use  of  to  transmit  a  musical 
note,  and  he  also  proposed  to  apply  this  discovery  so  as  to 
admit  of  the  simultaneous  transmission  of  several  messages 
on  the  same  wire.  Mr.  Varley  could  not  by  his  arrange- 
ment transmit  any  other  feature  of  the  sound  than  that 
transmitted  by  the  telephone  of  Reiss. 

Elisha  Gray  of  Chicago  practically  carried  out  the  appli- 
cation of  the  idea  of  Reiss  so  that  not  only  one  but  several 
messages  could  by  this  means  be  transmitted  along  one  line. 
In  doing  this  he  introduced  reeds  or  forks  tuned  to  a  given 
note,  which  made  and  broke  contact  at  the  sending  end  of 
the  circuit ;  at  the  receiving  station  the  sounding  magnet  was 
connected  with  a  resonating  chamber  tuned  to  the  note  of 
one  reed.  When  this  reed  was  set  in  action  the  resonating 
chamber  tuned  to  that  note  sounded,  but  the  others  were 
silent.  It  is  well  known  that  resonators  of  this  kind  can  be 
used  to  analyse  complex  sounds,  and  to  show  distinctly  of 
what  simple  tones  the  whole  sound  is  composed.  In  a 


Appendix  on  the  Telephone  and  Microphone.     373 

similar  way  the  resonators  on  the  telegraphic  circuit  analysed 
the  complex  waves  of  the  electrical  current  as  they  passed 
to  and  fro,  so  that  each  resonator  sounded  only  so  long  as 
a  given  reed  vibrating  to  the  same  note  continued  to  con- 
tribute its  successive  impulses  to  the  compound  current. 
Mr.  Gray  is  said  also  to  have  invented  a  method  by  which 
the  intensity  of  the  notes  as  well  as  their  musical  pitch 
could  be  reproduced  at  the  receiving  end. 

None  of  these  telephones  could  possibly  transmit  arti- 
culate speech.  Articulation  depends  not  only  on  the  number 
and  intensity  of  impulses  which  the  ear  receives  in  a  given 
time,  but  on  the  manner  in  which  each  impulse  increases 
and  decreases.  In  other  words,  articulation  depends  on  a 
quality  analogous  to  the  form  of  a  wave,  and  cannot  be 
produced  by  any  instrument  which  merely  indicates  the 

Fig.  175- 


number  of  waves  per  second,  or  even  their  height,  and 
number. 

The  vibrations  of  a  simple  disc  under  the  influence  ot 
waves  impinging  on  one  of  its  sides  and  produced  by  the 
human  voice,  follow  the  impulses  given  by  the  voice  with 
such  accuracy  that  if  they  are  reproduced  at  a  distance  by 
mechanical  means  on  a  similar  disc,  this  disc  will  set  the  air 
round  it  in  motion  so  as  to  reproduce  the  articulate  words. 
This  fact  is  shown  by  the  common  toy  well  known  long 
before  the  invention  of  the  electric  telephone.  This  toy 
consists  of  two  similar  stretched  skins  or  pieces  of  paper 
connected  by  a  string  as  in  Fig.  175. 

A  person  by  speaking  to  the  bladder  at  A  causes  move- 
ments of  the  bladder  which  follow  the  impulses  produced 
by  the  voice  accurately.  These  movements  are  transmitted 
by  the  string  to  the  second  bladder,  so  that  a  person  at  B 


374 


Electricity  and  Magnetism. 


can  hear  the  bladder  B  pronounce  the  words  spoken  into  the 
bladder  A.  We  need  not  think  of  the  sound  as  transmitted 
by  some  special  conducting  power  in  the  string ;  the  con- 
duction is  a  simple  mechanical  phenomenon.  Every  time 
the  bladder  at  A  is  pulled  to  the  right  it  pulls  the  bladder  at 
B  to  the  right,  and  every  time  the  bladder  at  A  is  pushed  to 
the  left  it  allows  the  bladder  at  B  to  spring  back  to  the  left. 
But  more  than  this,  during  each  excursion  to  right  or 
left  the  movements  of  the  bladder  B  follow  those  of  bladder 
A  perfectly,  so  that  whatever  law  the  motions  of  bladder  A 
may  follow  in  its  deviation  to  the  one  side  the  bladder  B 
will  also  move  according  to  that  law.  The  string  thus  not 
only  transmits  the  number  of  impulses  and  their  total  am- 
plitude to  B,  but  it  also  transmits  what  may  be  called  their 
wave  form.  It  is  this  last  quality  which  enables  the  toy  to 
produce  articulate  sounds.  Except  for  this  it  would  only 
transmit  musical  sounds,  and  those  imperfectly,  giving  the 
prime  tone  due  to  the  note,  but  without  imitating  in  any  way 
what  musicians  call  the  quality  of  the  sound.  Professor 
Graham  Bell  of  Boston,  son  of  the  well-known  Alexander 

Fig.  176. 


Melville  Bell  of  Edinburgh,  author  of  'The  System  of 
Visible  Speech,'  is  the  inventor  of  an  electrical  telephone 
which  transmits  articulate  speech  by  electrical  means  even 
more  perfectly  than  the  toy  described  above  transmits 


Appendix  on  the  Telephone  and  Microphone.     375 

speech  by  mechanical  means.  Moreover,  while  the  me- 
chanical transmission  is  only  possible  across  very  short 
distances,  the  electrical  transmission  has  been  effected  over 
hundred  of  miles  of  wire.  The  receiving  instrument,  as  in 
the  mechanical  toy,  is  identical  with  the  sending  instrument, 
and  in  its  simplest  form  is  shown  in  Fig.  176  ;  each  vibrating 
bladder  is  represented  by  a  thin  plate  of  iron  D  pinched 
between  a  mouthpiece  E  and  a  handle  L  of  wood.  This 
disc  is  usually  a  piece  of  what  is  called  '  ferrotype '  iron,  the 
iron  plate  used  in  a  special  form  of  photograph  known  as  a 
ferrotype.  The  disc  D  is  set  in  motion  by  the  voice  precisely 
as  the  bladder  is  set  in  motion  by  the  voice  in  the  toy. 
Behind  the  disc,  and  in  close  proximity  to  it,  is  placed  one 
pole  of  the  bar  magnet  M,  and  round  this  pole  the  ordinary 
silk  covered  wire  is  coiled  so  as  to  form  the  small  bobbin  B. 
The  two  ends  of  the  coil  are  led  to  the  terminals  c  and  c. 
The  wooden  case  L  serves  to  connect  all  the  parts,  and  acts 
as  a  handle  by  which  the  instrument  can  be  placed  before 
the  mouth  or  held  to  the  ear. 

When  the  wire  coils  of  the  two  instruments  form  part  of 
one  telegraphic  circuit,  any  movement  in  the  disc  D  of  one 
instrument  will  alter  the  magnetic  field  in  which  the  coil  B 
is  placed.  This  alteration  will  induce  a  current  of  elec- 
tricity in  the  circuit.  This  current  will  produce  a  corre- 
sponding alteration  in  the  magnetic  field  of  the  receiving 
instrument,  and  so  cause  a  movement  in  the  disc  D  of  that 
instrument.  This  movement,  if  the  wires  are  wound  in  the 
same  direction,  will  be  in  the  opposite  direction  to  that  of 
the  sending  disc  D,  but  will  closely  correspond  with  that 
movement  in  the  same  sense  in  which  the  movement  of 
the  receiving  bladder  of  the  mechanical  toy  corresponds 
with  the  movement  of  the  sending  bladder,  with  one  dif- 
ference. In  the  case  of  the  mechanical  toy  the  movements 
of  the  two  discs  will  be  nearly  equal,  whereas  in  the  case 
of  the  electrical  movement  the  movements  will  be  propor- 
tional to  one  another,  but  very  far  from  equal ;  that  of  the 


376  Electricity  and  Magnetism. 

sending  disc  will  be  immensely  greater  than  that  of  the 
receiving  disc.  The  currents  which  work  the  telephone  are 
currents  induced  by  the  motion  of  the  ferrotype  disc  which 
acts  as  an  armature  to  the  magnet.  The  movements  of  this 
disc  are  exceedingly  small,  and  the  induced  currents  are 
exceedingly  small,  but  they  rise  and  fall  so  as  to  produce  a 
movement  in  the  far  disc  which  is  proportional  to  the  move- 
ment in  the  near  disc.  The  sound  produced  by  the  far 
disc  possesses  therefore  every  character  of  the  sound  which 
moves  the  near  disc  except  that  of  loudness.  The  words  as 
received  are  very  perfectly  articulate,  but  so  faint  that  the 
instrument  must  be  held  close  to  the  ear  to  allow  them  to 
be  distinctly  heard.  This  fact  forms  a  considerable  draw-: 
back  to  the  utility  of  the  instrument,  which  in  its  present 
form  cannot  be  used  as  a  call. 

The  explanation  of  the  action  of  the  instrument  given 
above  agrees  with  that  given  by  its  inventor.  Some  curious 
facts  have,  however,  led  many  to  believe  that  this  explanation 
is  not  the  true  one.  It  has  been  discovered  that  instead  of 
a  thin  ferrotype  disc  of  iron  a  thick  plate  might  be  used, 
and  it  has  been  asserted  that  this  plate  could  not  possibly 
bend  enough  under  the  influence  of  the  voice  to  induce 
currents  by  its  deflections.  The  word  bend  may  be  quite 
inapplicable  to  such  a  case,  but  the  surface  opposite  the 
magnet  does  certainly  advance  and  recede,  or  it  would  not 
transmit  sound  to  the  air  in  contact  with  it.  This  alternate 
advance  and  recess  would  take  place  if  instead  of  a  f  plate 
we  had  a  rod  many  feet  or  many  yards  long.  A  far  more 
singular  fact  has  been  discovered  by  many  observers,  namely 
that  non -magnetic  and  even  non-conducting  substances 
might  be  used  instead  of  a  ferrotype  disc  in  the  receiving 
instrument,  and  lastly  that  the  receiving  instrument  will 
work,  though  very  feebly,  with  no  disc  whatever.  In  this 
case  it  seems  clear  that  the  Page  effect,  as  it  may  be  called, 
i.e.  the  noise  made  by  the  magnet  itself  as  its  particles 
rearrange  themselves  with  each  change  of  stress,  is  the  source 


Appendix  on  the  Telephone  and  Microphone.     377 

of  the  sound  heard.  This  sound  becomes  articulate  as 
soon  as  its  increase  and  decrease  follow  the  increase  and 
decrease  produced  by  the  voice  at  the  sending  end.  It  is 
obvious  that  when  the  currents  sent  are  those  due  to  Bell's 
disc,  the  sounds  from  the  Page  effect  must  approximately  at 
least  correspond  with  those  which  the  ferrotype  receiving 
disc  would  give  off.  Thus  when  the  ferrotype  receiving  disc 
is  present  we  hear  at  least  two  simultaneous  voices,  the 
voice  of  the  disc  which  is  strong,  and  the  voice  of  the  magnet 
which  is  weak.  When  for  the  ferrotype  disc  we  substitute  a 
wooden  plate,  this  plate  will  act  as  a  sounding  board  for  the 
Page  effect.  When  the  plate  is  a  conductor  currents  will 
be  induced  in  it  by  the  change  in  the  magnetic  field,  and 
these  will  tend  to  move  the  plate  in  such  a  way  as  to  give 
a  third  source  of  sound  which  might  be  called  the  Ampere 
effect.  A  fourth  source  may  be  due  to  the  sound  produced 
in  the  wire  itself  as  the  current  changes  in  intensity  ;  this 
sound  was  first  observed  by  M.  Delarive,  and  his  obser- 
vations have  been  lately  confirmed  by  Dr.  Ferguson  in 
Edinburgh. 

Mr.  Gott  at  St.  Pierre  proved  that  no  internal  molecular 
effects  are  required  to  explain  the  action  of  the  telephone, 
for  he  attached  a  sending  disc  to  the  coil  of  one  siphon 
recorder,  and  a  receiving  disc  to  the  coil  of  another  siphon 
recorder.  Speaking  to  the  first  disc  he  caused  the  coil  to 
vibrate  in  the  strong  magnetic  field  of  the  instrument,  and 
thus  currents  were  induced  which  moved  the  coil  of  the 
second  instrument ;  this  coil  worked  its  own  disc,  and  was 
heard  to  speak  plainly.  This  experiment  perfectly  corrobo- 
rates Mr.  Graham  Bell's  explanation  of  his  instrument,  but 
is  not  in  contradiction  with  the  other  fact  mentioned  above, 
that  the  Page  effect  in  the  receiving  instrument  occurs 
simultaneously  with  what  may  be  called  the  Graham  Bell 
effect.  It  must  be  clearly  understood  that  while  the  Page 
effect  may  be  made  the  means  of  producing  articulate 
sounds,  this  can  only  be  done  by  using  Graham  Bell's 


378  Electricity  and  Magnetism. 

arrangement,  and  could  not  be  done  by  any  arrangement 
known  before  the  date  of  his  invention. 

The  words  spoken  by  the  telephone  have  a  slightly  nasal 
intonation.  The  nasal  sound  is  said  by  Helmholtz  to  be 
characteristic  of  tones  from  which  the  even  partials  are 
absent.  An  effect  of  this  kind  might  be  expected  from  the 
vibrations  of  the  straight  rod  producing  the  Page  effect,  but 
the  main  cause  of  nasality  must  be  in  the  vibrating  disc,  for 
all  discs  have  this  nasal  peculiarity  whether  made  to  vibrate 
by  magnetic  or  mechanical  arrangements.  It  is  clear  that 
the  disc  fastened  at  its  periphery  is  not  free  to  follow  the 
impulses  of  the  voice  with  perfect  truth,  but  has  modes  of 
vibration  of  its  own  which  modify  the  sound. 

Professor  P.  G.  Tait  has  calculated  that  the  current 
which  works  the  telephone  is  about  a  thousand  million 
times  less  than  the  current  used  in  ordinary  telegraphic 
work. 

This  calculation  shows  that  if  the  vibrations  produced  by 
sound  be  employed  to  modify  the  resistance  in  a  telegraphic 
circuit  which  includes  a  telephone,  this  telephone  will  pro- 
duce a  corresponding  sound,  provided  the  change  in  resist- 
ance amounts  to  one  thousand  millionth  of  the  resistance 
of  the  whole  circuit. 

This  fact  allows  us  to  comprehend  the  marvellous  action 
of  the  telephone  made  by  Mr.  Edison,  and  of  the  micro- 
phone discovered  by  Professor  Hughes.  These  two  instru- 
ments act  on  the  same  principle,  namely,  that  a  variation  in 
the  resistance  of  a  voltaic  circuit  may  be  caused  by  the 
variation  of  pressure  between  two  surfaces  in  contact,  and 
that  this  variation  of  resistance  will  cause  a  corresponding 
motion  in  the  disc  of  a  telephone  included  in  the  circuit. 
In  the  microphone  the  telegraphic  circuit  includes  a  voltaic 
battery,  a  telephonic  receiver,  and  two  pieces  of  carbon  lightly 
pressed  together.  This  carbon  is  sometimes  '  metallized,'  or 
prepared  by  being  heated  white  hot,  and  plunged  in  mer- 
cury. Any  sound  the  vibrations  of  which  causes  the  one 


Appendix  on  the  Telephone  and  Microphone.    379 

carbon  to  press  more  or  less  strongly  on  the  other,  so 
modifies  the  resistance  of  the  circuit  as  to  set  the  telephonic 
receiver  in  action  and  reproduce  the  sound  by  means  of  its 
vibrating  disc. 

One  form  of  the  instrument  is  shown  in  fig.  177.  A  piece 
of  carbon,  c,  very  delicately  balanced  on  an  axle,  A,  rests 
lightly  on  a  second  pie*ce  of  carbon,  D  ;  the  apparatus  rests 
on  a  sounding-board,  B,  and  the  rest  of  the  circuit  is  arranged 
as  shown  with  the  voltaic  cells  at  F,  and  the  telephone  at  T. 

FIG.  177- 


With  this  arrangement,  a  fly  walking  over  the  board  causes 
sounds  to  be  heard  in  a  distant  telephone.  The  change  of 
pressure  producing  a  change  of  resistance  occurs  between 
c  and  D.  Many  experiments  on  telephonic  transmission, 
due  to  similar  causes,  have  already  been  tried.  Slight 
vibrations  between  a  pile  of  nails,  or  the  vibrations  in  a 
tube  full  of  cinders,  are  competent  to  transmit,  more  or 
less  perfectly,  intelligible  speech  or  musical  sounds,  and 
Mr.  E.  Blyth  of  Edinburgh  states  that  he  has  heard  sounds 
from  a  jar  of  cinders  which  acted  as  the  receiver  while 


380  Electricity  and  Magnetism. 

another  jar  of  cinders  acted  as  the  sender.  In  Mr.  Edison's 
telephone  the  change  of  resistance  was  caused  by  a  simple 
change  of  the  pressure  of  a  vibrating  diaphragm  on  a  com- 
pound conductor  of  metal  and  plumbago ;  this  pressure 
was  varied  by  the  vibrations  produced  by  the  voice. 

The  principle  of  continuity  is  common  to  Graham  Bell's, 
Edison's,  and  Hughes'  inventions. 


INDEX. 


ABS 

A  BSOLUTE    electromagnetic  capacity 
**•     from  throw  of  galvanometer,  268 

—  electrometer,  211 

principle  of  Sir  William  Thomson's, 

100 

—  electrometers,  definition  of,  21 

—  unit  of  force,  20 
work,  51 

—  units,  compared  with  others,  162 
Absorption,  apparent,  by  insulators,  90 

—  by  insulators,  effect  on  resistance,  257 

—  in  condensers,  98 

—  of  heat  at  hot  junction  of  thermo-elec- 
tric pair,  185 

from    current   through  unequally 

heated  metal,  186 
Accumulation  of  electricity  on  projections 

of  conductors,  17 

Acid  facilitates  electrolysis  of  water,  166     . 
Acids  behave  like  electronegative  ions,  167 
Addition  of  coils  joined  in  multiple  arc,  235 
Agonic  line,  definition  of,  127 
Air,  potential  of,  obtained  byaid  of  flame,  41 

how  to  observe,  368 

measured  by  electrometer,  210 

point  in,  40 

—  pressure  balanced  by  electric  force,  104 
diminution    of,  required   to  produce 

sparks,  104 

Alloys  and  metals,  specific  resistance  of, 
251 

Alphabet,  Morse,  301 

• —  of  Thompson's  siphon  recorder,  338 

Amalgamation  of  zinc  plates  in  galvanic 
cell,  220 

Ampere,  discovered  laws  of  attraction  and 
repulsion  between  currents,  58 

Ampere's  theory  of  forces  between  cur- 
rents, 136 

Amplitude  of  current  indicating  dots 
through  cables,  333 

Anode,  definition  of,  67 

Antimony,  diamagnetic,  113 


BAT 

Armature,  attraction  between  electromag- 
net and,  123 

—  of  a  magnet,  121 

—  Siemens',  for    magnetoelectric  arrange- 
ments, 287 

Armatures  or  coatings  of  condensers,  98 
Armstrong,     Sir     W  illiam ;    hydroelectric 

machine,  274 

Arrival  curve  of  current,  331 
Astatic  galvanometers,  193 
Atlantic  cable,  Anglo-American,  design  of, 

350 
(French),   elements   of  arrival   curve 

for,  331 

speed  of  signalling  through,  335 

Atmospheric  electricity,  distribution  of,  367 
Attraction    and    repulsion    due    to    static 

electricity,  i 
induction,   14 

—  between  currents,  56 

—  maximum,    between  electromagnet  and 
armature,  123 

Automatic  sender,  Wheatstone's,  318 
Axis,  magnetic,  109 


"DAIN'S  chemical  telegraph.  306 

— •  electric  clock,  366 
—  telegraph,  printing  solution  for,  306 
Balance,  Wheatstone's,  246 

—  theory  of,  245 

Bases  of  salts  behave   like  electropositive 

ions,  167 
Battery,  galvanic,   Bunsen's  and  Faure's, 

228 

—  chromate  of  potassium,  229 
Daniell's,  221 

gas,  213 

general  instructions  for  management 

of,  230 

Leclanche,  230 

Marie  Davy's  and  Grove's,  227 

1 Menotti's,  226 


3S2 


Index,. 


BAT 

Battery     galvanic,     sand,      Smee's    and 

Walker's,  211 

Thomson's  and  sawdust,  225 

—  how  to  measure  resistance  of,  239 

B.  A.  units,  158 

Bell  instrument  for  +  and  —  signals,  308 

Bells,  electric,  328 

Bennett's  electroscope.  204 

Bismuth  is  diamagnetic,  113 

Bohnenberger's  electroscope,  204 

Bridge,  Wheatstone's,  246 

Bright,  Sir  Charles  ;  bell  instruments,  308 

British  Association  experiments  on  electro-' 

magnetic  resistance  in  absolute  measure, 

Brush  discharge,  41 
Bunsen's  galvanic  cell,  228 


(CABLES,  design  of,  350 
V*     Capacity,    absolute    electromagnetic 
from  throw  of  galvanometer,  268 

—  for  electricity,  meaning  of,  96 

—  of  a  knot  of  cable,  formula  for,  256 

—  of  cores  of  cables,  349 

—  of   long    cylindrical    conductor    (insu- 
lated wire),  101 

—  of  spheres  and  opposed  flat  plates,  96 

—  specific  inductive,  97 

—  tests,  to  determine  position  of  fault,  357 

—  unit  of,  electromagnetic,  134 

— electrostatic,  96 

practical,  162 

Capacities  compared  by  throw  of  galvano- 
meter, 263 

Caselli's  copying  telegraph  instrument,  324 
Casts  taken  by  electro-deposits,  360 
Cautery  applied  by  electricity,  365 
Charge  on  spheres  and  opposed  plates,  96 

—  proportional  to  potential  of  conductor,  36 
Chemical    affinity,   relation  to  E.  M.  F.  re- 
quired to  produce  decomposition,  171 

—  reaction  source   of  power  in    galvanic 
cell,  54 

—  telegraph,  Bain's  Morse,  306 

—  theory  of  E.  M.  F.  169 
of  galvanic  cell,  23 

Chromate  of  potassium  galvanic  cell,  229 
Chronoscopes,  electric,  366 
Circuit,   inductive,   in  frictional  electrical 
arrangements,  273 

—  telegraphic,  299 

Circuits,  lengths  worked  by  relays,  311 
Circular    current    producing    rotation    of 

straight  current,  294 
Clark's   compound ;    used    in    submarine 

cables,  351 

—  insulators  for  land  lines,  344 

—  cell,  E.  M.  F.  of,  159 

Clarke's  magneto-electric  machine,  282 

Clocks,  electrical,  366 

Closed  circuit,  analogy  with  magnet  of,  138 

—  circuits,  forces  exerted  between,  138 
Cobalt  is  paramagnetic,  113 


COR 

Code,  Morse,  360 

—  single  needle  Morse,  308 
Coefficient  for  effect  of  temperature  on  G.  p., 

257 
metals,  253 

—  of   magnetic     induction     for     various 
materials,  124 

in  iron,  123 

Coercive    force,    effect    of  in   telegraphic 
apparatus,  314 

in  magneto-electric  machines,  286 

meaning  of,  115 

Coil  of  galvanometer,  best  form  of,  196 

—  rotating  in  uniform  magnetic  field,  elec- 
tromotive force  due  to,  151 

used  to  determine  resistance, 

I.S4 
Coils,  resistance,  first  notion  of,  86 

—  flat  spiral,  action  of  current  in,  60 

—  long  cylindrical  action  of  current  in,  59 

—  sizes  of  wire  used  in  galvanometer,  202 

—  used  to  increase  force  between  currents, 
58 

Compass,  mariner's,  369 
Compound  magnets,  114 
Condenser  attached  to  inductorium,  292 

—  capacity  of,  97 

—  definition  of,  20 

—  Varley's  system  of  signalling  with,  338 
Condensers,  absorption  in,  98 

—  compared  by  throw  of  galvanometer,  264 

differential  galvanometer,  265 

galvanometer  and  resistance  slide, 

265 
platymeter,  266 

—  used  to  fire  mines  or  torpedos,  364 
Conductivity,  definition  of,  236 

—  specific  ;  definition,  252 

Conductor,   effect  of   large    conductor  in 
electrical  machines,  274 

—  in  submarine  cable,  347 
Conservation  of  energy,  theory  of ;  applied 

to  thermoelectric  pair,  185 
Constant  of  a  galvanometer,  237 
Contact  between  dissimilar  substances  pro- 
duces electricity,  21 

wires,  one  class  of  fault,  351 

test  to  find  position  of,  358 

—  potential  series  ;  for  metals,  43 

—  theory  of  galvanic  cell,  22,  44 
Continuity,  want  of,  one  class  of  fault,  351 
Convection  of  heat  by  electricity,   186 
Conversion  of  British  into  metrical  units,  164 
Copper  and  zinc  single  fluid  cell,  E.  M.  F. 

of,  219 

—  called  positive  pole  of  galvanic  cell,  222 

—  resistance  in  cables,  test  of,   by  Wheat- 
stone's  bridge,  248 

—  specific  resistance  of,  in  cables,  254 
Copying  telegraph  instruments,  Bakewell's 

and  Caselli's,  324 

Cores  of  cables,  capacity  per  knot,  349 
formula  for  insulation  resistance  of, 

348 


Index. 


COR 

Cores    of    cables,     insulation    resistance 
changed  by  temperature,  255 

—  of  electromagnets    split    in  telegraphic 
apparatus,  313 

Cost  of  motive  power  due  to  electricity,  297 
Couple  exerted    on    magnet  by  magnetic 

field,  112 

Culley's  rules  for  iron  wire  on  land  lines,  341 
Current,  commencement  of,  in  any  circuit, 78 

—  constant ;  strength  equal  in  all  parts  of 
circuit,  77 

—  electromagnetic  unit  of,  117 

—  induced  by  motion  of  magnet,  69 
by  increase    or  decrease  of   neigh- 
bouring currents,  72 

by  motion  of  neighbouring  current,  70 

—  jnfluence  of  resistance  of  battery  on,  86 

—  intensity    of    magnetic    field    produced 
by,  117 

—  meaning  of  strength  of,  56 

—  nominal  direction  of  in  galvanic  circuit, 

—  of  electricity,  definition  of,  52 

—  produced  by  galvanic  cell,  53 

—  produces  rotation  of  a  second  current,  293 

—  resume  of  various  causes  producing,  80 

—  thermoelectric,  first  notion  of,  79 

—  transient,  in  broken  circuit,  79 
Currents  act  on  magnets  as  if  solenoids, 

60 

—  fundamental  experiments  on,  57 

—  Ampere's  theory  of  forces  between,  136 

—  Arrival  curve  for,  331 

—  force  between,  56 

—  heat  conductors,  66 

—  induction  by,  70 

—  made  to  rotate  by  magnets,  295 

—  magnetise  iron,  66 

—  measured  in  electromagnetic  measure  by 
Weber's  electrodynamometer,  139 

by  Kohlrausch's  method,  140 

in  terms    of   force    between    flat 

spirals,  141 

—  multiplication  of  force  between  ;  by  use 
of  coils,  58 

—  produce  a  magnetic  field,  113 
rotation  of  magnets,  295 


T)ANIELL'S  cell,    chemical    theory  of 

*^       E.   M.   F.  Of,   172 

• E.  M.F.  of;  in  electromagnetic  measure, 

159 
management  of,  224 

—  —  practical  construction  of,  221 
resistance  of,  225 

—  cells  of  low  resistance  ;  Thomson's  large 
trays,  225 

—  —  sawdust  used  in,  225 
Dash  and  Dot  Morse  signals,  301 
Dead  beat  galvanometer,  198 
Declination,  magnetic,  definition  of,  127 
Decomposition  of  electrolyte  by  currents, 

67 


ELE 

Deflections,  equal ;  indicate  equal  currents 

in  galvanometer,  190 
Density,  electric  ;  definition  of,  102 

—  of  electricity,  16 

—  on  opposed  surfaces  depends  on  differ- 
ence of  potential,  106 

Dial  telegraphic  instruments,  319 

Diamagnetic  substances,  coefficient  of  mag- 
netic induction  for,  124 

Diamagnetism,  meaning  and  examples  of, 
113 

Dielectric,  meaning  of,  18 

Dielectrics,  specific  inductive  capacity  of, 
97 

Difference  of  potential,  definition  of,  26 

—  of  potential  due   to  contact  of  zinc  and 
copper  ;  Thomson's  experiment,  45 

between  coatings  of  Leydenjar,  33 

Differential  galvanometer,   adjustment  of, 

200 
description  of,  83 

—  —  precautions  to  be  observed  in  using, 
242 

Dimensions  of  a  unit,  meaning  of  the  term, 

161 

Dip  of  magnet,  126 
Dipping  needle,  in 
Direction  of  current  induced  by  motion  of 

neighbouring  magnet,  70 
nominal,  from  galvanic  cell,  53 

—  of  deflection  of  magnet  under  influence 
of  currents,  61 

Discharge  of  electricity  by  points,  40 

—  by  brush  or  spark  not  subject  to  Ohm's 
law,  92 

—  by  points,  due  to  increased  density,  102 

—  silent,  105 

Discharging  keys  for  return  currents    in 

telegraphic  circuits,  312 
Distances  worked  by  relays,  511 
Distribution  of  charge   examined  by  proof 

plane,  15 

—  of  statical  charge,  unaffected  by  mass 
of  conductor,  6 

Dot  and  Dash,  Morse  signals,  301 
Dots,  effect  of,  sent  rapidly  through  sub- 
marine cable,  333 

Dry  pile,  used  with  electroscopes,  204 
Duplex  sending  on  telegraphic  lines,  324 


"C*  ARTH   currents,    cut  off  line  by  con- 

•^     densers,  339 

effect  of,  in  telegraphic  lines,  312 

—  difference  of  potential  between  various 
parts  of,  367 

—  function  of,  in  telegraphic  circuit,  299 

—  magnetic  properties  of  the,  109 

—  magnetisation  of  soft  iron  bar  by,  121 

—  potential  of ;  used  as  zero,  29 
Earth's  magnetic  force,  cause  of,  369 
Ebner's  machine  for  firing  mines,  364 
Electric  density  on   plates,  spheres,    and 

points,  102 


334 


Index. 


ELE 

Electric  light,  361 

—  series    of   insulators    each    positive    to 
successor,  9 

Electrical  machine,  description  of  frictional, 
271 

first  notion  of,  5 

Electricity,  atmospheric,  367 

—  charge  of,  3 

—  conveyed  by    convection    through  air ; 
sparks,  brushes,  92 

—  how  produced,  21 

—  positive  and  negative,  7 

—  quantity  of,  3 

—  velocity  of,  329 

—  vitreous  and  resinous,  2 
Electrification,  change  of  apparent  resist- 
ance in  cables,  due  to,  257 

Electrochemical  equivalent  of  water,  165 

—  equivalents,  169 
Electrodes,  definition  of,  49 
Electrodynamometer,  construction  of,  59 

—  theory  of  Weber's,  138 
Electrolysis,  description  of,  67 
Electrolyte,  definition  of,  44 
Electrolytes  decomposed  into  groups  called 

ions,  167 

Electromagnet,  definition  of,  120 
Electromagnetic  engine,  Froment's,  296 

—  force  at  centre  of  circular  coil,  135 

—  induction,  description  of,  69 

—  measure,  relation  of  volt,  ohm,  farad,  to 
absolute,  160 

—  ring  produces  no  magnetic  field,  121 

—  system  of  units,  dimensions  of,  164 

—  unit  of  current,   117 

—  units,  definition  of,  133 

—  ratio  to  electrostatic  units,  134 
Electrometer,  absolute  ;  211 

definition  of,  21 

principle  of  Sir  William  Thomson's, 

100 

—  Thomson's  quadrant,  205 
portable,  207 

—  used  to  ascertain  potential  of  air,  210 
Electromotive  force,  chemical  theory  of,  169 
definition  of,  48 

due   to    alteration   of    neighbouring 

current,  value  of,  155 
in  terms  of  heat  of  combination  and 

electrochemical  equivalent,  171 
on  closed  circuit  rotating  in  magnetic 

field,  152 
produced    in    conductor   moving   in 

magnetic  field,  148 
required  to  produce  decomposition,  1 70 

—  unit  of,  electromagnetic,  134 

electrostatic,  95 

practical,  162 

without  difference  of  potentials,  75 

—  series  for  metals,  43  > 
Electromotor,  Froment's  and  beam,  296 
Electromotors,  cost  of,  compared  with  heat 

engines,  297 
Electrophorus,  270 


FAU 
Electroplating,  359 

—  theory  of,  173 

'  Electropositive,'  meaning  of,  43 
Electroscope,  charged  by  induction,  15 

—  gold  leaf,  $ 

Electroscopes,  Bennet's,  Canton's,  Bohnen- 
berger's,  Peltier's,  204 

—  gold  leaf  and  Peltier  ;  used  to  compare 
difference  of  potential,  37 

Electrostatic  force,  relation  of,  to  density 
of  electricity  on  neighbouring  conductor, 
102 

—  inductive  machines,  275 

—  measure,  meaning  of,  94 

—  system  of  units,  dimensions  of,  164 

—  units,  actual  magnitude  of,  107 
equations  connecting,  108 

of   quantity    resistance    and    differ- 
ence of  potential,  or  E.  M.  F.,  94 
Electrotypes,  360 

—  theory  of,  173 

Elementary  substances  discovered  by  elec- 
trolysis, 173 

Elements,  electrochemical  equivalents  of, 
169 

series,  168 

E.  M.  F.  necessary  to  decompose  an  electro- 
lyte, 170 

of  cells,  how  affected  by  solution,  219 

of  Clark's  cell,  159 

of  copper  zinc,  single  fluid  cell,  219 

of  Daniell's  cell,  159 

in  electrostatic  measure, 

100 

of  Grove's  cell,  and  Bun<;en's,  226-8 

of  Marie  Davy's  cell,   227 

of  thermo-electric  pair,  relation  of,  to 

thermoelectric  power,  179 

per  foot  of  wire  in  secondary  coil  of 

inductorium,  289 

of  bismuth-antimony  thermo-electric 

pair,  183 

unit  of,  called  a  volt,  159 

Equality  between  +  and  —  electricity  due  to 
any  cause,  8 

Equator,  magnetic,  128 

Equipotential  surfaces  in  magnetic  field,  115 

Equivalents,  electrochemical,  169 

Evolution  of  heat  at  cold  junction  of  thermo- 
electric pair,  185 


J7ARAD  ;  unit  of  capacity,  160 
-1-       Faraday's  potential  series  of  metals 
plunged  in  solutions,  216 

—  how   to   find  position  of  fault  causing 
loss  of  insulation,  352 

Fault,    how    to    find    position   of   second 
method,  353 

—  or  loss  of  insulation,  position  found  by 
aid  of  return  wire,  354 

—  position  of;  found  by  simultaneous  tests 
at  two  ends  of  line,  355 

Faults,  description  and  behaviour  of,  356 


Index. 


385 


FAU 
Faults,  in  telegraph   lines ;    classification, 

351 

Faure's  galvanic  cell,  229 
Feilit=ch,  experiment  on  suction  of  iron  into 

coil,  145 

Field,  magnetic  definition  of,  in 
Flow  of  electricity  depends  on  difference  of 

potentials,  40 

Foot-pound,  relation  to  absolute  unit,  51 
Force  and  work,  units  of,  94 

—  experienced    by    conductor    moving  in 
magnetic  field,  147 

—  of  attraction  or  repulsion  between  elec- 
trified bodies,  95 

magnetic  poles,  1 10 

Friction      between     insulators      produces 

electricity,  i 
difference  of  potentials,  42 

—  of  water  suspended  in  steam  produces 
electricity,  274 

Frictional  and  voltaic  electricity,  compari- 
son between,  50 

—  electrical  machine,  271 

Frog,  contraction   of  muscles   by  electri- 
city, 365 

Froment  s  electromotor,  296 
Fuse  for  firing  mines  by  electricity,  363 

f  ALVANIC  battery  ;  cells  in  series  and 
^-*     multiple  arc,  87 

—  batteries,  chief  merits  of,  212 

—  cell,  first  notion  of,  22 

influence  of  resistance  of,  86 

produces  permanent  current,  53 

source  of  power  in,  54 

Galvanometer,  application  of  shunts  to,  201 

—  astatic,  193 

—  coils,  best  form  of,  196 

practical  construction  of,  202 

—  dead  beat,  198 

—  description  of  Thomson's  mirror,  62 

—  differential,  adjustment  of,  200 
first  notion  of;  83 

—  effect  of  resistance  of,  189 

—  graded  ;  Thomson's,  197 

—  marine,  Thomson's,  199 

—  shunted  ;  resistance  of,  235 

—  sine,  195 

Galvanometers,  definition  and  classification 
of,  187 

—  how  to  adjust  sensibility  of,  192 
zero  of,  193 

—  intensity  and  quantity,  190 

—  long  coil  and  short  coil,  190 

—  size  of  wire  used  in  coils  of,  202 

—  vertical,  188 

Gas  engines,  electricity  used  in,  366 

—  galvanic  cell,  213 

Gases,  luminous  currents  through  rarefied, 
292 

—  perfect  insulators,  85 

Gassiot's  experiments  on  discharges  through 
rarefied  gases,  292 


HUG 

Geissler's  tubes,   conduction  through  rare- 
fied gases  in,  93 
used  with  inductorium,  292 

German  silver  used  for  differential  galvano- 
meter, 200 

in  differential  galvanometer,  242 

for  resistance  coils,  86 

Gilding,  359 

Glass,  hygrometric  properties  of,  262 

—  insulators  for  land  lines,  343 

—  resistance  of,  250 

—  used  in  frictional  electrical  machine,  272 
Gold  leaf  electroscope,  37 

Graphite,  resistance  of,  259 

—  used  in  electric  lamp,  361 

in  Walker's  galvanic  cell,  212 

Gravitation  galvanic  cell,  227 

Grove's  cells  used  for  electric  light,  361 

—  galvanic  cell,  227 

Gutta-percha  core,  capacity  of,  per  knot,  349 
resistance    of  at    different  tempera- 
tures, 255 
insulation  resistance  per  knot,  348 

—  cores,  dimensions  of,  347 

—  moulds  for  electrotypes,  360 

—  resistance  of  ;  measured,  as  test,  238 

—  sheath ;    resistance    tested    by    Wheat- 
stone's  bridge,  248 

—  specific  inductive  capacity  of,  97 
resistance  of,  254 


T_J  EAT,  amount  of,  produced  by  current, 

--  generated  by  flow  of  electricity,  41 

—  mechanical  equivalent    of,    in    various 
units,  165 

—  of  combination,   relation  to  E.  M.  F.  of, 
170 

—  of  fixed  stars  detected  by  thermoelectric 
battery,  185 

—  relation  of,  to  mechanical  work,  41 

—  transformed-into  electricity  by  thermo- 
electric pair,  185 

Helix,  intensity  of  magnetic  field  inside, 

142 

Heterostatic  electrometers,  204 
Holmes'  electric  lamp,  363 

—  (T. ),  magneto-electric  machine,  285 
Holtz'  inductive  electrostatic  machine,  277 
Homogeneous    wire,    used    in    submarine 

cables,  350 

Hooper's   india-rubber,  specific  resistance 
of,  254 

—  material,  insulation  resistance  per  knot 
of  core,  349 

capacity  per  knot  of  wire,  349 

Horizontal  component  of  earth's  magnetic 

force  ;  definition,  128 

determination  of,  128 

value  of,  131 

Horse-shoe  magnet,  121 

Hughes'  printing  telegraphic  instrument, 

323 


CC 


386 


Index. 


HYD 

Hydroelectric    machine    of    Sir    William 

Armstrong,  274 
Hygroscopic  properties  of  glass,  26-2 


of, 


INCLINATION,  magnetic  definition 

India-rubber,   core,  capacity  of  per  knot, 
electromagnetic,  256 

—  -------  electrostatic,  102 

---  resistance  of,  per  knot,  255 

—  specific  inductive  capacity  of,  97 
--  resistance  of,  254 

Induced  charge,  relation  of,  to  difference 
of  potential,  35 

—  current  due  to  change  in  neighbouring 
currents,  72 

--  reaction  of,  on  inducing  current,  73 
Induction,  electromagnetic,  in  broken  cir- 

cuit, 75 
---  in  long  circuit  of  considerable  capa- 

city, 76 

—  •  —  produces  E.  M.  F.,  75 

—  magnetic,  113 

—  magneto-electric,  281 

—  of  current  on  itself,  74 

—  of  currents  by  motion  of  magnet,  69 

—  statical,  ^description  of,  n 

--  produces  difference  of  potential,  41 
Inductive  capacity  of  materials,  specific,  97 

—  circuit  in  frictional  electrical  machine, 
273 

—  electrostatic  machines,  275 
--  machine  by  Holtz,  277 

—  retardation,  effect  of,  on  duplex  sending, 
328 

Inductprium  or  Ruhmkoff's  coil,  289 

—  luminous  discharges  from,  292 

—  make  and  break  apparatus  for,  291 

—  practical  construction  of,  290 
Inertia,  effect  of,  on  moving  parts  of  tele- 

graphic instruments,  118 

—  of  parts,  defects   in  telegraphic   appa- 
ratus due  to,  314 

Influence,  name  given  to  electromagnetic 

induction,  72 
Ink-writer,  Morse,  303 
Insulating    materials,  resistance  of,  com- 

pared with  conductors,  85 
Insulation  ;  causes  of  defective  insulation 

in  cables  and  land  lines,  351 

—  of  galvanometer  coils,  205 

—  resistance,  change  due  to  electrification, 
257 

---  meaning  and  calculation  of,  254 

--  of  glass,  259 

--  of  land  lines,  346 

--  per  knot  of  cable  cores,  348 

—  test,  by_  fall  of  potential,  255 

---  by  simple  galvanometer  deflections, 

238 
--  by  Wheatstone's  bridge,  248 

—  tests,  precautions    to    be  observed   in 
making,  262 


LIG 

|    Insulators,   change    of   resistance   due  to 
temperature,  256 

—  specific  inductive  capacity  of,  97 

—  used  for  land  lines,  343 
Intensity,  galvanic  cells  joined  for,  88 

—  of  magnetisation,  definition  of,  112 

—  galvanometers,  190 

—  of  magnetic  field,  in 

inside  circular  coil  and  helix, 

142 
produced  by  curient  in  straight 

wire,  117 
Interior    of   bodies,    contains   no    statical 

charge,  16 

Inversions,  thermoelectric,  177 
Ions,  definition  of,  67 

—  do  not   combine  during  their  passage 
through  solutions,  173 

—  electro-positive  and  electro-negative,  167 
Iron  filings  used  to  show  lines  offeree,  119 

—  magnetised  by  currents,  66 

—  soft,  meaning  of,  114 

—  wire,  specific  resistance  of,  254 
Isoclinic  lines,  definition  of,  128 


JOULE'S  mechanical  equivalent  of  heat, 
J      4i 


T^  ATHODE,  definition  of,  67 
•"•*•     Key  Morse,  300 

—  reversing,  307 

—  single  needle, -I- and — ,  307 

Keys  for  transmitting,  magnetoelectric,  288 

Killing  iron  wire,  meaning  of,  342 

KirchhofFs  laws,  248 

—  applied  to  Wheatstone's  bridge,  250 

Knot  of  submarine  cable,  insulation  resist- 
ance of,  255 

capacity  of,  255 

resistance  of  conductor  in,  254 

Kohlrausch's  method   of    measuring   cur- 
rents in  electromagnetic  measure,  140 


T   AND  lines,  contact  between  wires  on, 

—  insulation,  resistance  of,  346 

insulators  for,  343 

theory  of  signalling  through,  334 

wire  for,  341 

Lead,  used  as  standard  thermo-electric 
metal,  176 

Leclanche  galvanic  cell,  230 

Lenz's  laws,  70 

Leyden  jar  attached  to  inductorium,  202 

either  coating  may  be  to  earth,  37 

description  of,  18 

used  in  connection  with  electro- 
meters, 206 

—  jars,  changes  of  potential  due  to  con- 
nection between,  36 

Light,  electric,  361 


Index. 


387 


circuit, 


LIG 
Lightning  causes  death  without  striking, 

365  . 

—  conductors,  action  of,  105 

—  one  form  of  electric  spark,  93 
Lines  of  force  in  magnetic  field,  in 
direction  of,  shown  by  iron  filings, 

119 

—  due  to  thin  bar  magnet,  1 1 1 

used  to  calculate  E.  M.  p.,  due  to 

motion  in  magnetic  field,  150 
indicate    direction   and    intensity 

of  magnetic  field,  116 

—  telegraphic,  general  description  of,  340 
Liquids,  electrolysis  chiefly  confined  to,  166 
• —  form  thermo-electric  pair,  184 

Local  action  in  galvanic  cell,  220 

Loss  of  charge  used  as  insulation  test,  255 

—  of  insulation,  one  class  of  fault,  351 
Luminous  currents  through  rarefied  gases, 

292 

TVTAGNET;  analogy  with  closed 

with  solenoid,  60 

—  effect  of  change  in  dimension  on  attrac- 
tion to  armature,  125 

—  causes  rotation  of  current,  295 

—  made  to  rotate  by  current,  295 

—  poles,  axis,  109 

Magnetic  declination,  definition  of,  127 

—  field,  at  centre  of  circular  current  and 
long  helix,  142 

definition  of,  in 

due  to  earth,  description  of,  126 

how  to  determine  intensity  of, 

128 

—  value  of  horizontal  compo- 
nent of  force  in,  131 

to  electric  current,  113 

E  M.F.  produced  in  conductor  moving 

in,  148 

force  experienced  by  conductor  mov- 
ing in,  147 

unit,  in 

—  force,  earth's,  possible  cause  of,  369 

—  inclination,  definition  of,  126 

—  induction,  113 
coefficient  of,  123 

—  meridian,  definition  of,  127 

—  moment,  definition  of,  112 

—  moments  compared  by  times  of  oscilla- 
tion, 132 

—  potential,  115 

—  storms,  meaning  of,  128 
Magnetization  by  magnetic  field,  112 

—  increase  or  decrease  of,  induces  currents, 
70     _ 

—  maximum  intensity  of,  in  iron,  123 

—  of  iron  by  currents,  66 
Magneto-electric  arrangements,   Siemens' 

armature  for,  287 

—  —  Morse  sender,  316 
induction,  281 

machine,  Clark's  and  Pixii's,  282 


NEG 

Magneto-electric  machine,  limit  to  E.M.F. 
in,  286 

• by  T.  Holmes,  284 

power  required  to  drive,  286 

Wild's,  Siemens',  Ladd's,  Wheat- 
stone's,  287 

transmitting  keys,  288 

Magneto  sender  lor  dial  instruments,  321 
Magnets,  action  of  currents  on,  60 

—  adjusting  ;  for  galvanometer,  193 

—  how  made,  119 

—  how  suspended  in  galvanometers,  193 

—  if  broken  ;  pieces  are  magnets,  119 
Marie  Davy's  galvanic  cell,  227 
Marine  galvanometer,  Thomson's,  199 
Matthiessen  ;  experiments  on  resistance  of 

metals  and  alloys,  251 
Matthiessen's  thermo-electric  series,  176 
Mechanical  equivalent  of  heat,  41 
Medical  applications  of  electricity,  364 
Megavolt,  megohm,  megofarad,  161 
Melloni ;  used  thermo-electric  battery  as 

thermometer,  184 
Menotti's  galvanic  cell,  226 
Meridian,  magnetic,  definition  of,  127 
Metallurgy,  application  of  electricity  10,359 
Metals  and  alloys,  specific  resistance  of,  251 
Microfarad  ;  unit  of  capacity,  159 
Microphone,  378 

Microvolt,  microhm,  microfarad,  161 
Mines  fired  by  electricity,  363 
Mirror  galvanometer,  signalling  with,  335 

formula  for  speed  of  signalling  by,  340 

Moment,  magnetic  definition  of,  112 

of  long  thin  bar,  122 

of  sphere,  123 

—  of  inertia,  129 

of  body,  how  to  find,  131 

—  of  magnet,  experimental  determination 
of,  130 

Morse  chemical  telegraph,  Bain's,  306 

—  circuit,  302 

—  inkwriter,  303 

—  key,  300 

—  maximum  speed  of  possible  signals,  340 

—  signals,  300 

rate  of  hand  sending,  318 

—  sounder,  signals  received  by  ear,  307 
Motive  power  produced  by  electricity,  cost 

of,  297 
Moulds  for  casts,  made  by  deposited  metals, 

360 
Multiple  arc,  cells  joined  in,  87 

meaning  of,  235 

resistance  between  points  joined  by,  235 


]V[  EGATIVE  and  positive  currents  ;  defi- 
•^      nition,  300 

electricity,  7 

signals,  302    • 

—  ions  chemically  electro-,  167 

—  ;  list  of  insulators  negative  relatively  to 
others,  9 


383 


Index. 


NEG 

Negative  ;  list  of  metals  electro-negative  to 
others,  43 

—  metals  ;  thermo-electrically,  175 

—  pole  of  galvanic  battery,  222 

—  thermo-electric  power,  definition,  179 
Nickel  is  paramagnetic,  113 

Nitric  acid,  diluted,  specific  resistance  of, 
262 


r~\HM  name  given  to  unit  of  resistance, 

^     158 

Ohm's  law,  82 

applied  to  potential  at  various  parts 

of  circuit,  243 

—  not  applicable  to  brushes  or  sparks,  92 
Ores,  reduction  of,  by  electrolysis,  361 
Oxides  when  fused  are  electrolytes,  166 


TDAPER,  punched,  strips  used  in  auto- 
matic transmitter,  318 
Paraffin,  specific  inductive  capacity  of,  97 
Paramagnetism,  meaning  of;  list  of  para- 
magnetic bodks,  113 
Peltier  effect,  in  thermo-electric  pair,  185 

—  electroscope,  38 

Physiological  effects  of  electricity,  364 
Pile,  dry,  used  with  electroscopes,  204 
Pith  ball,  experiments  with,  4 
Pixii's  magneto-electric  machine,  282 
Platinum  and  platinized  silver  in  galvanic 

cell,  211 

—  used  for  contacts,  316 

Piatymeter,  used  to  compare  condensers, 

266 
Pliicker's     experiments     on    sparks    with 

spectroscope,  292 

Plugs  used  to  make  connections,  231 
Points,  action  of,  in  electrical  machines, 

272 

—  in  lightning  conductors,  105 

—  discharge  highly    charged  conductors, 
274 

—  discharge  positive  and  negative  electri- 
city unequally,  106 

Polarization  due  to  electrolysis  resembles 
increased  resistance,  89 

—  in  galvanic  cells,  213 

—  in  insulators,  connected  with  absorption, 
98 

resembles  increased  resistance,  90 

—  of  faults,  356 
Polarized  relay,  311 

Pole,  strength  of  magnetic  unit,  no 

Poles  for  land  lines,  342 

• —  magnetic,  description  of,  109 

—  of  magnets,  not  at  ends,  119 

—  positive  and  negative  of  Daniell's  cell,-?22 
Porcelain  insulators  for  land  lines,  343 
Porous  cells,  used  in  two  fluid  batteries,  221 
Portable  electrometer,  Thomson's,  207 
Positive  and  negative  currents,  definition, 

300 


RAT 

Positive  and  negative  electricity,  7 

signals,  302 

. —  instruments  for,  307 

—  ions  chemically  electro-,  167 

—  ;  list  of  insulators  positive  relatively  to 
others,  9 

of  metals  electropositive  to  others,  43 

—  metals,  thermo-electrically ;  definition,  1 75 

—  pole  of  galvanic  cell,  222 

—  thermo-electric  power  ;  definition,  179 
Potential,  contact  series,  43 

—  definition  of,  26 

—  difference  of,  measurement  in  units  of 
work,  31 

—  equality  of,  29 

—  fall  of,  used  to  calculate  insulation  resist- 
ance, 255 

—  general  conception  of,  10 

—  magnetic,  115 

—  of  a  point,  29 

—  of  a  point  in  the  air,  40 

—  of  air,  how  to  observe,  368 

—  of  statically  charged  conductor  is  uni- 
form, 31 

—  on  what  it  depends,  30 

—  series  ;  of  metals  dipped  in  solutions,  216 

—  unit  of,  electromagnetic,  134 

•  —  electrostatic,  95 

practical,  162 

—  zero  of,  10 

Potentials,  practical  mo_des  of  comparing,  269 
Power  required  to  drive  magneto-electric 

machine,  286 
Pressure,  effect  of,  on  insulation  resistance, 

255 
Primary  coil  in  inductorium,  289 

—  wire,  definition,  155 

Printing,  step  by  step  telegraphic  instru- 
ment, 323 

—  telegraph  instrument,  Hughes',  323 
Proof  plane,  15 

Punched  paper  used  to  send  signals,  318 


P)UADRANT  electrometer,  Thomson's, 
>C     205 

Quantity,  electromagnetic  unit  (absolute), 
«34 

—  electrostatic  unit  (absolute),  20 

—  force  of  attraction  or  repulsion  due  to,  95 

—  galvanic  cells  joined  for,  88 

—  galvanometers,  190 

—  in  a  charge  depends  on  difference   of 
potential,  96 

—  in  short  current  measured  by  throw  of 
galvanometer,  269 

—  of  electricity  measured  by  measuring 
force,  20 

—  practical  unit  for,  162 


13  AREFIED  gases,  resistance  of,  93 
J^-     Rate  of  sending   by  automatic  and 
hand  transmitters,  318 


Index. 


339 


REG 

Recorder,  Thomson's  siphon,  336 
Rectangle  of  wire  used  to  illustrate  force 

between  currents,  57 

Return  currents,  in  telegraphic  circuits,  312 
Relay  ;  definition,  309 
Relays,  diagram  of  circuit  with,  310 

—  length  of  circuit  worked  by,  311 
• —  polarized,  311 

v —  various  constructions  of,  310 
.Replenisher,  description  of  Thomson's  in- 
ductive, 277 

—  used  in  electrometers,  207 
Repulsion  between  currents,  56 

—  electric  charges,  4 

Residual  magnetism,  effect  of,  in  tele- 
graphic apparatus,  314 

meaning  of,  115 

Resistance  and  potential,  relation  between, 
in  circuit  conveying  current,  243 

—  apparent,  various  forms  of,  89 

—  between  points  joined  by  multiple  arc,  235 

—  calculated  from  loss  of  charge,  255 

—  coils,  arrangement  of  boxes  of,  231 

—  first  description  of,  86 

practical  instructions  for  making,  233 

—  electric,  definition  of,  81 

—  insulation,  calculation  of,  254 

—  per  knot  in  submarine  cables,  255 

—  measured  by  Wheatstone's  bridge,  246 

—  measurement  of,  by  comparison  of  deflec- 
tions, 236 

by  shunted  differential  galvano- 
meter, 241 

—  object  of  determining,  86 

—  of  cables,  effect  of  electrification  on,  257 
- —  of  copper  per  knot  in  submarine  cables, 

254 

—  of  insulators  and  conductors  compared, 
85 

—  apparently  changed  by  flow  of  cur- 
rent, 90 

measured  as  a  test,  238 

effect  of  age  and  pressure  on,  255 

temperature  on,  256 

G.  P.  india-rubber,  254 

—  of  galvanic  battery,   how   to  measure, 
239 

cell,  limits  currents,  86 

—  of  galvanometer,  effect  of,  on  current  in 
given  circuit,  89 

coils,  202 

—  of  gases,  infinite,  85 

—  of  graphite  and  gas  coke,  tellurium  and 
phosphorus,  259 

—  of  large  Daniell's  tray  cells,  226 

—  of  liquid  electrolytes,  260 

—  of  metals,  effect  of  temperature  on,  253 
increased  by  impurities,  253 

—  of  rarefied  gases,  93 

—  of  shunted  galvanometer,  235 

—  of  vacuum,  93 

—  per  knot  of  insulated  cere,  348 

—  precautions  to  be  observed  in  measuring 
small,  247 


SIN 

Resistance,  relation  to  length  and  cross 
section  of  conductors,  83 

to  weight,  per  unit  of  length,  of  con- 
ductor, 84 

—  slide,  used  to  compare  condensers,  266 

—  specific,  definition,  250 

—  —  of  metals  and  alloys,  251 

—  unit  of,  electromagnetic,  134 

electrostatic,  95 

practical,  162 

Reverse  currents,  useful  in  working  land- 
lines,  311 

Reversing  key  for+and— signals,  307 
Rheomotor,  definition,  299 
Rotation  of  one  current  by  another,  293 

—  of  current  by  magnet  and  magnet  by 
current,  295 

Ruhmkoff's  coil  or  inductorium,  289 

used  to  send  current  through  rarefied 

gas  ;  Geissler  tubes,  93 


C  ALTS,  fused,  form  thermo-electric  pairs, 

—  when  fused,  are  electrolytes,  166 
Sand  battery,  211 

Saturation,  meaning  of,  as  applied  to  mag 

nets,  120 

Sawdust  galvanic  battery,  225 
Screen,  metal,  between  electrified  bodies, 

effect  of,  24 
Secondary  coil  in  inductorium,  289 

—  wire  ;  definition,  155 
Self-induction  in  resistance  coils,  234 

—  of  current  on  itself,  74 

Sensibility  of  galvanometer,  adjusted  by 
shunt,  201 

how  adjusted,  192 

Series,  electric  contact  ;  metals,  42 

—  electro-chemical,  168 
frictional  ;  insulators,  9 

—  galvanic  cells  joined  in,  87 

—  Matthiessen's  thermo-electric,  176 

—  of  insulators,each  positive  to  successor,  9 

—  potential,    metals   dipped   in  solutions, 
216 

Shunt,  definition  of,  201 

—  used  to  adjust  sensibility  of  galvano- 
meter, 201 

Shunted  galvanometer,  resistance  of,  235 
Siemens'  and  Frischen's  duplex  telegraphic 
systems,  328 

—  armature  for  magneto-electric  arrange- 
ments, 287 

—  experiments  on  effect  of  temperature  on 
resistance  of  metals,  253 

—  polarized  relay,  311 
Signalling,  theory  of,  331 

—  with  condensers,  338 

Signals,  telegraphic,  elements  of,  300 
T—  Morse,  300 
Sine  galvanometer,  195 
Single  fluid  galvanic  cells,  polarization  in, 
215 


390 


Index. 


SIN 

Single  needle  instrument,  307 

key,  307 

Morse  code,  308 

Siphon  recorder,  Thomson's,  336 
Smee's  battery,  212 
Soft  iron,  meaning  of,  114 
Solenoid  ;  analogy  with  magnet,  60 

—  definition  of,  60 

—  does  not  in  all  respects  resemble  hollow 
magnet,  145 

—  effect  of  introducing  soft  iron  into,  146 

—  magnetic  moment  of,  144 

—  suction  of  iron  or  magnet  into,  144 
Sounder,  Morse,  signals  received  by  ear, 

3°  7 

Source  of  power  in  galvanic  cell,  54 
Sparks  and  brushes  convey  electricity  in 

modes  not  subject  to  Ohm's  law,  92 

—  diminution  of  air  pressure  required  to 
produce,  104 

—  pierce  solid  insulators,  106 

—  weld  contacts  together,  316 

Specific  inductive  capacity  of  dielectrics,97 

—  resistance  of  a  material,  definition,  250 
of  insulators  used  in  cables,  254 

changed  by   temperature    and 

electrification,  257 

of  electrolytes,  260 

of  glass,  259 

of    graphite,   gas     coke,    tellurium, 

phosphorus,  259 

—  resistances  of  metals  and  alloys,  251 
Speed  of  working  on  land  lines,  318 

—  of  signalling  through  submarine  lines, 

—  by  mirror  or  siphon,  formula  for, 
340 

by  Morse,  340 

Spiral  coils,  flat,  attraction  and  repulsion 

between,  60 
Spirals,  conveying  currents  force,  between, 

flat,  141 

Statical  induction,  description  of,  u 
Steam's  duplex  telegraphic  system,  326 
Steel,  coercive  force  of,  120 
Step  by  step  printing  instruments,  323 

—  telegraph  instruments,  319 
Stoneware  insulators  for  land  lines,  343 
Stratified  discharge  through  rarefied  gas, 

292 

Street's  fusible  alloy,  360 
Strength  of  a  current,  56 

—  of  constant  current  equal  in  all  parts  of 
circuit,  77 

—  of  magnetic  poles  ;  definition,  no 
Submarine  cables,  design  of,  350 

—  practical  formulae  for  speed  through, 

34° 
theory  of  signalling  through,  329 

—  line,  speed  of  signalling  through,  335 
Sulphate   of  copper  in    solution,    specific 

resistance  of,  261 

—  of  zinc  in  solution,  specific  resistance  of, 
261 


THO 

Sulphuric  acid,  diluted,  specific  resistance 
of,  261 

used  in  electrometers,  206 

Surface  conduction,  or  creeping  on  in- 
sulators, 262 

Synchronous  motion  in  Hughes'  printing 
instruments,  323 


TRAIT'S  thermo-electric  table,  182 
•*•      Tangent  galvanometer,  best  construc- 
tion of,  194 

—  galvanometer,  theory  of,  135 
Telegraphic  apparatus  ;  classification,    298 
general  remarks  on,  313 

—  circuit,  299 
Telephone,  371 

—  Edison's,  378 

—  strength  of  currents  in,  378 
Temperature,  effect  of  on  resistance,  85 

insulators,  256 

metals,  253 

—  measured  by  thermo-electric  battery,  184 
Test  of  copper  resistance  by  Wheatstone's 

bridge,  248 

—  of  insulation  by  measuring  resistance  ; 
simple  galvanometric  method,  238 

—  by  Wheatstone's  bridge,  248 
Tests  of  iron  wire,  mechanical,  342 

—  for  positions  of  faults,  352 
Thermal  equivalent  of  work,  165 
Thermo-electric     bismuth-antimony    pair, 

E.  M.  F.  of,  183 

—  circuit,  absorption  and  evolution  of  heat 
in  unequally  heated  portions  of,  186 

—  current,  first  notion  of,  79 

—  currents  due  to  liquids  and  to  fused  salts, 
184 

—  diagram,  178 

—  E.  M.  F.,  calculation  of  from  diagram.  180 

—  Tail's  table,  181 

—  inversions,  177 

—  neutral  points,  181 

—  pair,  absorption  and  evolution  of  heat  at 
junctions  of,  185 

Peltier  effect  in,  185 

theory  of,  in  complex  circuit,  176 

—  pairs  in  series,  183 

—  power,  connection  between   E.  M.  F.  of 
pair  and,  179 

of  a  pair  of  metals  ;  definition,  175 

—  powers,  ii  luence  of  mean  temperature 
on,  177 

—  series,  Matthiessen's,  176 
Thomson's  absolute  electrometer,  principle 

of,  100 

—  dead-beat  galvanometer,  198 

—  graded  galvanometer,  197 

—  marine  galvanometer,  199 

—  method    of   determining    resistance    in 
electromagnetic  measure,  154 

—  mirror  galvanometer,  62 

—  replenisher,   and  mouse-mill    inductive 
machines,  277 


Index.  • 


391 


THO 
Thomson's  siphon  recorder,  336 

—  theory  of  convection  of  heat  by  electri- 
city, 186 

—  theory  of  signalling,  333 

Throw  of  galvanometer  compares  poten- 
tials, 269 

—  gives  absolute   electro-magnetic 
capacity,  268 

—  used  to  compare  capacities,  263 
measures  quantity  in  transient  cur- 
rent, 269 

Time-guns,  366 

Time  required  for  any  electrical  operation 
in  signalling,  339 

Torpedos  fired  by  electricity,  364 

Tourmaline,  effect  of  temperature  on,  49 

Transmission  of  signals  in  two  directions  on 
one  line,  325 

Trembler  ;  one  kind  of  electric  bell,  329 


T  TNI  FORM   potential  throughout  con- 

ductors,  31 

Uninsulated  bodies,  definition  of,  10 
Unit  electromotive  force,  how  produced  by 
motion  in  magnetic  field,  149 

—  intensity  of  magnetic  field,  in 

—  magnetic  pole,  no 

—  of  capacity  called  microfarad,  159 

—  of  current  electro-magnetic,  117 

—  of  electromotive    force    called   a  volt, 
!59 

•  —  —  in  terms  of  Clark's  cell,  159 

• •  — of  Daniell's  cell,  159 

—  of  force  and  work  (absolute),  94 

—  of  quantity,  20 

—  is   farad   charged   to  potential  of 
one  volt,  1 60 

—  of  resistance  called  an  ohm,  158 

—  of  work  used  to  measure  potential,  26 

—  quantity,  resistance  and  E.  M.  p.,  or  diff. 
of  potential,  definition  of,  electrostatic,  94 

—  table  of  absolute  and  practical,  162 
Units,  British  Association,  158 

—  dimensions  of,  163 

—  electro-magnetic,  definition  of,  133 

—  ratio  to  electrostatic  units,  134 

—  electrostatic,  actual  magnitude  of,  107 

—  equations  connecting,  108 


WARIATIONS  of  magnetic  declination 

and  inclination,  127 

Varley's  electrostatic  inductive   machine, 
276 

—  insulators  for  land  lines,  344 

—  rule  for  insulation  of  land  lines,  347 

—  system  of  sending  Morse  signals  with 
reverse  currents,  311 


ZIN 

Varley's   system   of  signalling  with  con- 
denser, 338 

Velocity  of  electricity,  330 
Volt,  name  given  to  unit  of  E.  M.  p.,  159 
Voltaic,  arc,  meaning  of,  362 

—  of  contact  theory  of  galvanic  cell,  44 
Voltameter,  166 

Vulcanite  insulators  for  land  lines,  345 

—  or  ebonite  used  for  electrophorus,  270 

—  stems,  used  to  insulate,  262 

—  used  for  frictional  electrical  machines,272 
for  mountings  of  resistance  boxes,  231 


VyALKER'S  graphite  battery,  212 
v  v      Waring 's  electric  light,  363 
Water   and  electricity,  analogy  between, 
used  to  explain  potential,  39 

—  electro-chemical  equivalent  of,  165 

—  decomposition  of,  67 

Weber,  name  given  by  Latimer  Clark  to 

unit  quantity,  160 
Weber's  electro-dynamometer,   theory  of, 

138 
Weight  of  materials  required    for    given 

speed  of  signalling  (submarine  lines),  340 
Wheatstone's  automatic  transmitter,  318 
- —  bridge,  used  to  measure  resistance ;  246 

—  theory    of,    proved    by    KirchliofFs 
laws,  250 

—  letter-showing  dial   telegraphic   instru- 
ments, 322 

Wild's  magneto-electric  machine,  287 
Willoughby  Smith's  G.  P.  effect  of  tem- 
perature on  resistance  of,  258 

—  gutta-percha,  specific  inductive    ca- 
pacity of,  97 

Wire,  sizes  used  in  galvanometers,  63 
of,  used  in  galvanometer  coils,  202 

—  of,  for  telegraphic  apparatus,  316 

—  iron,  employed  on  land  lines,  341 

—  weight  and  mechanical  qualities  of, 
342 

Wires,  spacing  of  on  land  lines,  342 
Words  per  minute  through  submarine  lines, 

34° 
Work,  and  force,  units  of,  94 

—  —  —  absolute  and  other  units  compared; 
British  and  metrical,  165 

—  mechanical,  relation  to  electric  poten- 
tial, 27 

—  positive  and  negative,  27 

—  used  to  measure  difference  of  potential, 


lates,  amalgamation  of,  220 

;    wire     in    connection  with  in 

negative  pole  of  battery,  2 


Spottisvtoodt  <§°  Co.,  Printers,  New-street  Square,  London. 


V 


